Finite Group Databasebeta

← Group #72317737

Character table — Group #72317737

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222224444444444448888888888888888161616161616161616161616161616161616161616161616161616161616161616161616161616161616161632323232323232326464646464646464646464646464
order12442224442222224444442222224444448888222444444444448888888888888888888888888888888888888844444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111-1-11-1-11111-1-1-1-111-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-11-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1
χ71111111111111111111111111111111111-1-1-1-11-1-11-1-11111-1-1-1-1-1-1111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ81111111111111111111111111111111111-1-1-1-11-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111
χ9111111111111111111111111-1-111111-1-111111-111-111-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ10111111111111111111111111-1-111111-1-111111-111-111-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ11111111111111111111111111-1-111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111
χ12111111111111111111111111-1-111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ13111111111111111111111111-1-111111-1-11-1-1-1-1-111-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1
χ14111111111111111111111111-1-111111-1-11-1-1-1-1-111-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-111
χ15111111111111111111111111-1-111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ16111111111111111111111111-1-111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1
χ1722222222222222-2-2-2-22222-2-2222-22-2-222-20000200200-2-2-2-200000022-2-200000000000022-2-20000000000000000000000002-20000
χ1822222222222222-2-2-2-22222-2-2222-22-2-222-20000200200-2-2-2-2000000-2-222000000000000-2-222000000000000000000000000-220000
χ1922222222222222-2-2-2-22222-2-2-2-22-22-2-2-2-2-20000-200-200222200000022-2-200000000000022-2-2000000000000000000000000-220000
χ2022222222222222-2-2-2-22222-2-2-2-22-22-2-2-2-2-20000-200-2002222000000-2-222000000000000-2-2220000000000000000000000002-20000
χ21222222222222-2-2222222-2-2-2-200-22-22-200-222220000000000000022000022-2-20000-2-2-2-2000022-2-20000000000002-2000000000000
χ22222222222222-2-2222222-2-2-2-200-22-22-200-2222200000000000000220000-2-2220000-2-2-2-20000-2-222000000000000-22000000000000
χ23222222222222-2-2222222-2-2-2-200-22-22-200-2-2-2-2-200000000000000-2-2000022-2-200002222000022-2-2000000000000-22000000000000
χ24222222222222-2-2222222-2-2-2-200-22-22-200-2-2-2-2-200000000000000-2-20000-2-222000022220000-2-2220000000000002-2000000000000
χ252222222222-2-2222222-2-2222-200-2-2-2-2200-2000000000000000000002222222200000000-2-2-2-2-2-2-2-20000-2-222000000000000000000
χ262222222222-2-2222222-2-2222-200-2-2-2-2200-2000000000000000000002222-2-2-2-200000000-2-2-2-22222000022-2-2000000000000000000
χ272222222222-2-2222222-2-2222-200-2-2-2-2200-200000000000000000000-2-2-2-22222000000002222-2-2-2-2000022-2-2000000000000000000
χ282222222222-2-2222222-2-2222-200-2-2-2-2200-200000000000000000000-2-2-2-2-2-2-2-200000000222222220000-2-222000000000000000000
χ292222222222-2-222-2-2-2-2-2-222-2200-22-22-20020000000000000000000022-2-2000022220000-2-2220000-2-2-2-20000000000000000002-200
χ302222222222-2-222-2-2-2-2-2-222-2200-22-22-20020000000000000000000022-2-20000-2-2-2-20000-2-22200002222000000000000000000-2200
χ312222222222-2-222-2-2-2-2-2-222-2200-22-22-200200000000000000000000-2-22200002222000022-2-20000-2-2-2-2000000000000000000-2200
χ322222222222-2-222-2-2-2-2-2-222-2200-22-22-200200000000000000000000-2-2220000-2-2-2-2000022-2-2000022220000000000000000002-200
χ332222222222-2-2-2-22222-2-2-2-2-22002-22-2-200200000220220000-2-2-2-200000022-2-2000000000000-2-222000000000000002-20000000000
χ342222222222-2-2-2-22222-2-2-2-2-22002-22-2-200200000220220000-2-2-2-2000000-2-22200000000000022-2-200000000000000-220000000000
χ352222222222-2-2-2-22222-2-2-2-2-22002-22-2-200200000-2-20-2-20000222200000022-2-2000000000000-2-22200000000000000-220000000000
χ362222222222-2-2-2-22222-2-2-2-2-22002-22-2-200200000-2-20-2-200002222000000-2-22200000000000022-2-2000000000000002-20000000000
χ3722-2-2222-2-2-2222222-2-2-2-2-2-2-2-22222-2-22-2-222i2i−2i−2i200-20022-2-200002i−2i0000000000002i2i−2i−2i00000000000000002i2i−2i−2i00000000000000
χ3822-2-2222-2-2-2222222-2-2-2-2-2-2-2-22222-2-22-2-22−2i−2i2i2i200-20022-2-20000−2i2i000000000000−2i−2i2i2i0000000000000000−2i−2i2i2i00000000000000
χ3922-2-2222-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-222222i2i−2i−2i-200200-2-22200002i−2i0000000000002i2i−2i−2i0000000000000000−2i−2i2i2i00000000000000
χ4022-2-2222-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-22222−2i−2i2i2i-200200-2-2220000−2i2i000000000000−2i−2i2i2i00000000000000002i2i−2i−2i00000000000000
χ4122-2-2222-2-2-22222-2-222-2-2-2-222222-2-22-2-2-2-2000022-2-22-2-2-22222-2-20000000000000000000000000000000000000000002-200000000
χ4222-2-2222-2-2-22222-2-222-2-2-2-222222-2-22-2-2-2-200002-22-2-22-2-222-2-222000000000000000000000000000000000000000000-2200000000
χ4322-2-2222-2-2-22222-2-222-2-2-2-222-2-22-2-22-222-20000-22-222-222-2-222-2-2000000000000000000000000000000000000000000-2200000000
χ4422-2-2222-2-2-22222-2-222-2-2-2-222-2-22-2-22-222-20000-2-222-2222-2-2-2-2220000000000000000000000000000000000000000002-200000000
χ4522-2-2222-2-2-222-2-222-2-2-2-2222200-222-2-200-22i2i−2i−2i000000000000002i−2i000000002i2i−2i−2i−2i−2i2i2i000000002i2i−2i−2i000000000000002-2000000
χ4622-2-2222-2-2-222-2-222-2-2-2-2222200-222-2-200-22i2i−2i−2i000000000000002i−2i00000000−2i−2i2i2i−2i−2i2i2i00000000−2i−2i2i2i00000000000000-22000000
χ4722-2-2222-2-2-222-2-222-2-2-2-2222200-222-2-200-2−2i−2i2i2i00000000000000−2i2i000000002i2i−2i−2i2i2i−2i−2i000000002i2i−2i−2i00000000000000-22000000
χ4822-2-2222-2-2-222-2-222-2-2-2-2222200-222-2-200-2−2i−2i2i2i00000000000000−2i2i00000000−2i−2i2i2i2i2i−2i−2i00000000−2i−2i2i2i000000000000002-2000000
χ4922-2-2222-2-2-2-2-2-2-2-2-2222222-220022-2-2200-2000002-202-20000-2-22200000000002i2i−2i−2i000000000000−2i−2i2i2i000000000000000000002i−2i
χ5022-2-2222-2-2-2-2-2-2-2-2-2222222-220022-2-2200-2000002-202-20000-2-2220000000000−2i−2i2i2i0000000000002i2i−2i−2i00000000000000000000−2i2i
χ5122-2-2222-2-2-2-2-2-2-2-2-2222222-220022-2-2200-200000-220-22000022-2-200000000002i2i−2i−2i000000000000−2i−2i2i2i00000000000000000000−2i2i
χ5222-2-2222-2-2-2-2-2-2-2-2-2222222-220022-2-2200-200000-220-22000022-2-20000000000−2i−2i2i2i0000000000002i2i−2i−2i000000000000000000002i−2i
χ53444444444444-4-4-4-4-4-444-4-44400-4-4-4-440040000000000000000000000000000000000000000000000000000000000000000000000
χ544444444444-4-4-4-4-4-4-4-4-4-4-4-44-4004444400-40000000000000000000000000000000000000000000000000000000000000000000000
χ554444-44-4-44-400004-44-400000022000002200000-200-2002-22-2000000000000002-22-200000000004-42-22-20000000000000000000000
χ564444-44-4-44-400004-44-400000022000002200000-200-2002-22-200000000000000-22-220000000000-44-22-220000000000000000000000
χ574444-44-4-44-400004-44-4000000-2-200000-2-200000200200-22-22000000000000002-22-20000000000-442-22-20000000000000000000000
χ584444-44-4-44-400004-44-4000000-2-200000-2-200000200200-22-2200000000000000-22-2200000000004-4-22-220000000000000000000000
χ594444-44-4-44-40000-44-4400000022000002200000-200-200-22-22000000000000002-22-2000000004-400-22-220000000000000000000000
χ604444-44-4-44-40000-44-4400000022000002200000-200-200-22-2200000000000000-22-2200000000-44002-22-20000000000000000000000
χ614444-44-4-44-40000-44-44000000-2-200000-2-2000002002002-22-2000000000000002-22-200000000-4400-22-220000000000000000000000
χ624444-44-4-44-40000-44-44000000-2-200000-2-2000002002002-22-200000000000000-22-22000000004-4002-22-20000000000000000000000
χ634444-4-44-4-44004-40000004-4000000000000222202-20-2200002-22-2-2-20000000000002-22-2004-4000000000000000000000000000000
χ644444-4-44-4-44004-40000004-400000000000022220-2202-20000-22-22-2-20000000000002-22-200-44000000000000000000000000000000
χ654444-4-44-4-44004-40000004-4000000000000-2-2-2-202-20-2200002-22-222000000000000-22-2200-44000000000000000000000000000000
χ664444-4-44-4-44004-40000004-4000000000000-2-2-2-20-2202-20000-22-2222000000000000-22-22004-4000000000000000000000000000000
χ674444-4-44-4-4400-44000000-44000000000000222202-20-220000-22-22-2-2000000000000-22-224-400000000000000000000000000000000
χ684444-4-44-4-4400-44000000-4400000000000022220-2202-200002-22-2-2-2000000000000-22-22-4400000000000000000000000000000000
χ694444-4-44-4-4400-44000000-44000000000000-2-2-2-202-20-220000-22-22220000000000002-22-2-4400000000000000000000000000000000
χ704444-4-44-4-4400-44000000-44000000000000-2-2-2-20-2202-200002-22-2220000000000002-22-24-400000000000000000000000000000000
χ7144-4-4444-4-4-444-4-4-4-444-4-444-4-400-4-44440040000000000000000000000000000000000000000000000000000000000000000000000
χ7244-4-4444-4-4-4-4-44444-4-444-4-4-4400-4-444400-40000000000000000000000000000000000000000000000000000000000000000000000
χ7344-4-4444-4-4-4-4-444-4-44444-4-44-400-444-4-40040000000000000000000000000000000000000000000000000000000000000000000000
χ7444-4-4444-4-4-4-4-4-4-444-4-444444-4004-4-44-40040000000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-44-44-4400004-4-440000002200000-2-200000-2002002-2-220000000000004i−4i2i−2i−2i2i0000000000002i−2i−2i2i0000000000000000000000
χ7644-4-4-44-44-4400004-4-440000002200000-2-200000-2002002-2-22000000000000−4i4i−2i2i2i−2i000000000000−2i2i2i−2i0000000000000000000000
χ7744-4-4-44-44-4400004-4-44000000-2-2000002200000200-200-222-20000000000004i−4i−2i2i2i−2i000000000000−2i2i2i−2i0000000000000000000000
χ7844-4-4-44-44-4400004-4-44000000-2-2000002200000200-200-222-2000000000000−4i4i2i−2i−2i2i0000000000002i−2i−2i2i0000000000000000000000
χ7944-4-4-44-44-440000-444-40000002200000-2-200000-200200-222-200000000004i−4i002i−2i−2i2i000000000000−2i2i2i−2i0000000000000000000000
χ8044-4-4-44-44-440000-444-40000002200000-2-200000-200200-222-20000000000−4i4i00−2i2i2i−2i0000000000002i−2i−2i2i0000000000000000000000
χ8144-4-4-44-44-440000-444-4000000-2-2000002200000200-2002-2-2200000000004i−4i00−2i2i2i−2i0000000000002i−2i−2i2i0000000000000000000000
χ8244-4-4-44-44-440000-444-4000000-2-2000002200000200-2002-2-220000000000−4i4i002i−2i−2i2i000000000000−2i2i2i−2i0000000000000000000000
χ8344-4-4-4-4444-4004-4000000-440000000000002i2i−2i−2i0220-2-200002-2-22−2i2i004i−4i000000002i−2i−2i2i0000000000000000000000000000000000
χ8444-4-4-4-4444-4004-4000000-440000000000002i2i−2i−2i0-2-20220000-222-2−2i2i00−4i4i000000002i−2i−2i2i0000000000000000000000000000000000
χ8544-4-4-4-4444-4004-4000000-44000000000000−2i−2i2i2i0220-2-200002-2-222i−2i00−4i4i00000000−2i2i2i−2i0000000000000000000000000000000000
χ8644-4-4-4-4444-4004-4000000-44000000000000−2i−2i2i2i0-2-20220000-222-22i−2i004i−4i00000000−2i2i2i−2i0000000000000000000000000000000000
χ8744-4-4-4-4444-400-440000004-40000000000002i2i−2i−2i0220-2-20000-222-2−2i2i4i−4i0000000000−2i2i2i−2i0000000000000000000000000000000000
χ8844-4-4-4-4444-400-440000004-40000000000002i2i−2i−2i0-2-202200002-2-22−2i2i−4i4i0000000000−2i2i2i−2i0000000000000000000000000000000000
χ8944-4-4-4-4444-400-440000004-4000000000000−2i−2i2i2i0220-2-20000-222-22i−2i−4i4i00000000002i−2i−2i2i0000000000000000000000000000000000
χ9044-4-4-4-4444-400-440000004-4000000000000−2i−2i2i2i0-2-202200002-2-222i−2i4i−4i00000000002i−2i−2i2i0000000000000000000000000000000000
χ9188888-8-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000004-4000000000000000000
χ9288888-8-88-8-800000000000000000000000000000000000000000000000000000000000000000000000000-44000000000000000000
χ9388-8-88-8-8-8880000000000000000000000000000000000000000000000000000000000000000000000004i−4i00000000000000000000
χ9488-8-88-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000−4i4i00000000000000000000
χ958-88i−8i0000004-40000004i−4i00004-4000004i−4i04ζ−4ζ4ζ3−4ζ30000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000000000
χ968-88i−8i0000004-40000004i−4i00004-4000004i−4i0−4ζ4ζ−4ζ34ζ3000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000000000
χ978-88i−8i0000004-40000004i−4i0000-4400000−4i4i04ζ−4ζ4ζ3−4ζ3000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000000000
χ988-88i−8i0000004-40000004i−4i0000-4400000−4i4i0−4ζ4ζ−4ζ34ζ30000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000000000
χ998-8−8i8i0000004-4000000−4i4i00004-400000−4i4i04ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000000000
χ1008-8−8i8i0000004-4000000−4i4i00004-400000−4i4i0−4ζ34ζ3−4ζ4ζ000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000000000
χ1018-8−8i8i0000004-4000000−4i4i0000-44000004i−4i04ζ3−4ζ34ζ−4ζ000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000000000
χ1028-8−8i8i0000004-4000000−4i4i0000-44000004i−4i0−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000000000
χ10316-1616i−16i000000-88000000−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10416-16−16i16i000000-880000008i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.