
<!-- %W  construc.xml    GAP 4 package CTblLib              Thomas Breuer -->
<!-- %Y  Copyright 2011, Lehrstuhl D für Mathematik, RWTH Aachen, Germany -->


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Chapter Label="chap:constructions">
<Heading>Functions for Character Table Constructions</Heading>

<#Include Label="construc:intro">


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="sec:construc:MGA">
<Heading>Character Tables of Groups of Structure <M>M.G.A</M></Heading>

For the functions in this section,
let <M>H</M> be a group with normal subgroups <M>N</M> and <M>M</M>
such that <M>H/N</M> is cyclic, <M>M \leq N</M> holds,
and such that each irreducible character of <M>N</M>
that does not contain <M>M</M> in its kernel
induces irreducibly to <M>H</M>.
(This is satisfied for example if <M>N</M> has prime index in <M>H</M>
and <M>M</M> is a group of prime order that is central in <M>N</M>
but not in <M>H</M>.)
Let <M>G = N/M</M> and <M>A = H/N</M>,
so <M>H</M> has the structure <M>M.G.A</M>.

For some examples, see <Cite Key="Bre11"/>.

<#Include Label="PossibleCharacterTablesOfTypeMGA">
<#Include Label="BrauerTableOfTypeMGA">
<#Include Label="PossibleActionsForTypeMGA">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="sec:construc:GS3">
<Heading>Character Tables of Groups of Structure <M>G.S_3</M></Heading>

<#Include Label="CharacterTableOfTypeGS3">
<#Include Label="PossibleActionsForTypeGS3">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="sec:construc:GV4">
<Heading>Character Tables of Groups of Structure <M>G.2^2</M></Heading>

<#Include Label="construc:GV4">

<#Include Label="PossibleCharacterTablesOfTypeGV4">
<#Include Label="PossibleActionsForTypeGV4">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="sec:construc:V4G">
<Heading>Character Tables of Groups of Structure <M>2^2.G</M></Heading>

<#Include Label="construc:V4G">

<#Include Label="PossibleCharacterTablesOfTypeV4G">
<#Include Label="BrauerTableOfTypeV4G">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="sec:construc:subdirindex2">
<Heading>Character Tables of Subdirect Products of Index Two</Heading>

<#Include Label="construc:subdirindex2">

<#Include Label="CharacterTableOfIndexTwoSubdirectProduct">
<#Include Label="ConstructIndexTwoSubdirectProduct">
<#Include Label="ConstructIndexTwoSubdirectProductInfo">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="sec:construc:preg">
<Heading>Brauer Tables of Extensions by <M>p</M>-regular Automorphisms
</Heading>

<#Include Label="construc:preg">

<#Include Label="IBrOfExtensionBySingularAutomorphism">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="sec:construc:cenex">
<Heading>Character Tables of Coprime Central Extensions</Heading>

<#Include Label="CharacterTableOfCommonCentralExtension">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="sec:construc:functions">
<Heading>Construction Functions used in the Character Table Library</Heading>

<#Include Label="construc:functions">

<#Include Label="ConstructMGA">
<#Include Label="ConstructMGAInfo">
<#Include Label="ConstructGS3">
<#Include Label="ConstructV4G">
<#Include Label="ConstructProj">
<#Include Label="ConstructDirectProduct">
<#Include Label="ConstructCentralProduct">
<#Include Label="ConstructSubdirect">
<#Include Label="ConstructWreathSymmetric">
<#Include Label="ConstructIsoclinic">
<#Include Label="ConstructPermuted">
<#Include Label="ConstructAdjusted">
<#Include Label="ConstructFactor">
<!-- ConstructClifford -->

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<!--
<Section Label="sec:construc:misc">
<Heading>Miscellaneous</Heading>

%FileHeader[8]{construc}

%Declaration{PossibleActionsForTypeGA}

</Section>  -->

<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->

</Chapter>

