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##
#W  example1.g               XMOD example files                 Chris Wensley
#W                                                                & Murat Alp
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#H  $Id: k4d6.g,v 2.006 2004/09/06 gap Exp $
##
#Y  Copyright (C) 1999,2001 University of St. Andrews, North Haugh,
#Y                          St. Andrews, Fife KY16 9SS, Scotland
##
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K4 := Group( (1,2)(3,4), (1,3)(2,4) );
aK4 := AutomorphismGroup( K4 );
Print( "The generating set for aK4 has two superfluous elements:\n" );
gaK4 := GeneratorsOfGroup( aK4 );
Print( gaK4, "\n" );
SetName( K4, "K4" );
SetName( aK4, "D6" );
XK4 := XModByAutomorphismGroup( K4 );
Print( "The crossed module XK4 :-\n" );
Display( XK4 );
Print( "Create the cat1-group CK4 associated to the crossed module XK4.\n" );
CK4 := Cat1OfXMod( XK4 );
Display( CK4 );
Print( "Source group of CK4 is a semidirect product with D6 acting on K4.\n");
sdp := Source( CK4 );
gensdp := GeneratorsOfGroup( sdp );
Print( "The generators of this sdp are\n", gensdp, "\n" );
Print( "The result is the symmetric group S4? " );
Print( IdGroup( sdp ) = IdGroup( SymmetricGroup( 4 ) ), "\n" );
