Finite Group Databasebeta

← Group #72265280

Character table — Group #72265280

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size1111111122222222222244444444888888888888888888881616161616161616161616161616161616161616161616161616161616161616161632323232323232323232323232323232646464646464646464646464
order12224444222222444444224444442444444488888888888822224444444444448888888888888888884444888888888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ9111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-111-1-111-1-1
χ10111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111
χ11111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111
χ12111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-11111-1-111-1-1
χ13111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1
χ14111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-111-1-1-1-111
χ15111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ16111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-111-1-1-1-11111-1-1
χ172222222222222222222222-2-222-2-22-2-2-2-2-22-222222222-2-2-2-2220022000000-2-2-2-2-2-2-2-20000-2-2222200000000000000000000000000000000
χ182222222222222222222222-2-222-2-22-2-2-2-2-22-222222222-2-2-2-2-2-200-2-2000000222222220000-2-2-2-2-2-200000000000000000000000000000000
χ192222222222222222222222-2-222-2-22-2-2-2-2-22-2-2-2-2-2-2-2-2-22222220022000000-2-2-2-22222000022-2-2-2-200000000000000000000000000000000
χ202222222222222222222222-2-222-2-22-2-2-2-2-22-2-2-2-2-2-2-2-2-22222-2-200-2-20000002222-2-2-2-2000022222200000000000000000000000000000000
χ2122222222222222222222-2-222-2-222-222-2-2-2-2-22222-2-2-2-2222200000000222200000000-2-2-2-2-2-200000000-2-200000000000022000000000000
χ2222222222222222222222-2-222-2-222-222-2-2-2-2-22222-2-2-2-2222200000000-2-2-2-2000000002222-2-20000000022000000000000-2-2000000000000
χ2322222222222222222222-2-222-2-222-222-2-2-2-2-2-2-2-2-22222-2-2-2-20000000022220000000022222200000000-2-2000000000000-2-2000000000000
χ2422222222222222222222-2-222-2-222-222-2-2-2-2-2-2-2-2-22222-2-2-2-200000000-2-2-2-200000000-2-2-2-222000000002200000000000022000000000000
χ2522222222222222222222-2-2-2-2-2-2-2-2-2-2-2222-222222-2-2-2-2-2-2-2-2002200220000000000000000220000-2-2-2-200-2-2220000000000000000000000
χ2622222222222222222222-2-2-2-2-2-2-2-2-2-2-2222-222222-2-2-2-2-2-2-2-200-2-200-2-2000000000000000022000022220022-2-20000000000000000000000
χ2722222222222222222222-2-2-2-2-2-2-2-2-2-2-2222-22-2-2-2-222222222002200220000000000000000-2-20000222200-2-2-2-20000000000000000000000
χ2822222222222222222222-2-2-2-2-2-2-2-2-2-2-2222-22-2-2-2-22222222200-2-200-2-20000000000000000-2-20000-2-2-2-20022220000000000000000000000
χ29222222222-2-2-2-22-2-2-2-22222222222-2-2-222-2-2-222-2-222-2-222-2-20000000000000000000000002-20000000000000000000000002-22-200000000
χ30222222222-2-2-2-22-2-2-2-22222222222-2-2-222-2-2-222-2-222-2-222-2-20000000000000000000000002-2000000000000000000000000-22-2200000000
χ31222222222-2-2-2-22-2-2-2-22222222222-2-2-222-2-2-2-2-222-2-222-2-222000000000000000000000000-220000000000000000000000002-2-2200000000
χ32222222222-2-2-2-22-2-2-2-22222222222-2-2-222-2-2-2-2-222-2-222-2-222000000000000000000000000-22000000000000000000000000-222-200000000
χ33222222222-2-2-2-22-2-2-2-22222-2-222-2-2-222-2-22-2222-2-222-2-2-2-222000000000000000000000000-220000000000000022-2-222-2-200000000000000
χ34222222222-2-2-2-22-2-2-2-22222-2-222-2-2-222-2-22-2222-2-222-2-2-2-222000000000000000000000000-2200000000000000-2-222-2-22200000000000000
χ35222222222-2-2-2-22-2-2-2-22222-2-222-2-2-222-2-22-22-2-222-2-22222-2-20000000000000000000000002-20000000000000022-2-2-2-22200000000000000
χ36222222222-2-2-2-22-2-2-2-22222-2-222-2-2-222-2-22-22-2-222-2-22222-2-20000000000000000000000002-200000000000000-2-22222-2-200000000000000
χ37222222222-2-2-2-22-2-2-2-222-2-222-2-2222-2-2-2-222222-2-2-2-22222-2-2000000000000000000000000-22000000000000000000000000000000002-22-2
χ38222222222-2-2-2-22-2-2-2-222-2-222-2-2222-2-2-2-222222-2-2-2-22222-2-2000000000000000000000000-2200000000000000000000000000000000-22-22
χ39222222222-2-2-2-22-2-2-2-222-2-222-2-2222-2-2-2-2222-2-22222-2-2-2-2220000000000000000000000002-2000000000000000000000000000000002-2-22
χ40222222222-2-2-2-22-2-2-2-222-2-222-2-2222-2-2-2-2222-2-22222-2-2-2-2220000000000000000000000002-200000000000000000000000000000000-222-2
χ41222222222-2-2-2-22-2-2-2-222-2-2-2-2-2-2-2-222222-22-222-2-2-2-222-2-2220000000000000000000000002-200000000000000000000000000002i−2i2i−2i0000
χ42222222222-2-2-2-22-2-2-2-222-2-2-2-2-2-2-2-222222-22-222-2-2-2-222-2-2220000000000000000000000002-20000000000000000000000000000−2i2i−2i2i0000
χ43222222222-2-2-2-22-2-2-2-222-2-2-2-2-2-2-2-222222-22-2-2-22222-2-222-2-2000000000000000000000000-2200000000000000000000000000002i−2i−2i2i0000
χ44222222222-2-2-2-22-2-2-2-222-2-2-2-2-2-2-2-222222-22-2-2-22222-2-222-2-2000000000000000000000000-220000000000000000000000000000−2i2i2i−2i0000
χ452222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-222-22-2-2-220000000000000000000022-2-200002i2i−2i−2i0000002i2i−2i−2i2i2i−2i−2i2-2002i−2i0000000000000000000000
χ462222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-222-22-2-2-220000000000000000000022-2-20000−2i−2i2i2i000000−2i−2i2i2i−2i−2i2i2i2-200−2i2i0000000000000000000000
χ472222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-222-22-2-2-2200000000000000000000-2-22200002i2i−2i−2i0000002i2i−2i−2i−2i−2i2i2i-2200−2i2i0000000000000000000000
χ482222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-222-22-2-2-2200000000000000000000-2-2220000−2i−2i2i2i000000−2i−2i2i2i2i2i−2i−2i-22002i−2i0000000000000000000000
χ492222-2-2-2-2222222-2-2-2-2-2-222-2-2-2-2222-22-222-2-2000000000000002200-2-2000000002i2i−2i−2i2i2i−2i−2i00−2i−2i2i2i0000002-200000000002i−2i000000000000
χ502222-2-2-2-2222222-2-2-2-2-2-222-2-2-2-2222-22-222-2-2000000000000002200-2-200000000−2i−2i2i2i−2i−2i2i2i002i2i−2i−2i0000002-20000000000−2i2i000000000000
χ512222-2-2-2-2222222-2-2-2-2-2-222-2-2-2-2222-22-222-2-200000000000000-2-20022000000002i2i−2i−2i−2i−2i2i2i00−2i−2i2i2i000000-220000000000−2i2i000000000000
χ522222-2-2-2-2222222-2-2-2-2-2-222-2-2-2-2222-22-222-2-200000000000000-2-2002200000000−2i−2i2i2i2i2i−2i−2i002i2i−2i−2i000000-2200000000002i−2i000000000000
χ532222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-22-2-2222-20000000000002222-2-2-2-222-2-222-2-2000000000000000000-22-22000000000000000000000000
χ542222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-22-2-2222-200000000000022-2-2-2-222-2-22222-2-20000000000000000002-22-2000000000000000000000000
χ552222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-22-2-2222-2000000000000-2-22222-2-2-2-222-2-2220000000000000000002-2-22000000000000000000000000
χ562222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-22-2-2222-2000000000000-2-2-2-2222222-2-2-2-222000000000000000000-222-2000000000000000000000000
χ572222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-22222-2-222-2-2220000000000002200-2-2000000-2-22200002i2i−2i−2i000000−2i−2i2i2i00002i−2i00000000−2i2i000000000000
χ582222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-22222-2-222-2-2220000000000002200-2-2000000-2-2220000−2i−2i2i2i0000002i2i−2i−2i0000−2i2i000000002i−2i000000000000
χ592222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-22222-2-222-2-222000000000000-2-2002200000022-2-200002i2i−2i−2i0000002i2i−2i−2i0000−2i2i00000000−2i2i000000000000
χ602222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-22222-2-222-2-222000000000000-2-2002200000022-2-20000−2i−2i2i2i000000−2i−2i2i2i00002i−2i000000002i−2i000000000000
χ614444-4-4-4-44-4-4-4-444444-4-44444-4-4-4-4-4-444-444-400000000000000000000000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-44-4-4-4-444444-4-444-4-4-4-444-44-4-44-44400000000000000000000000000000000000000000000000000000000000000000000000000
χ634444-4-4-4-44-4-4-4-444444-4-4-4-44444-4-44-44-44-4-4400000000000000000000000000000000000000000000000000000000000000000000000000
χ644444-4-4-4-44-4-4-4-444444-4-4-4-4-4-4444444-44-44-4-400000000000000000000000000000000000000000000000000000000000000000000000000
χ654444-4-4-4-4-444-4-4-444-4-444000000000000000000004-44-4000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000
χ664444-4-4-4-4-444-4-4-444-4-444000000000000000000004-44-400000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000
χ674444-4-4-4-4-444-4-4-444-4-44400000000000000000000-44-44000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000
χ684444-4-4-4-4-444-4-4-444-4-44400000000000000000000-44-4400000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000
χ694444-4-4-4-4-4-4-444-4-4-44444000000000000000000004-4-44000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ704444-4-4-4-4-4-4-444-4-4-44444000000000000000000004-4-4400000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ714444-4-4-4-4-4-4-444-4-4-4444400000000000000000000-444-4000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ724444-4-4-4-4-4-4-444-4-4-4444400000000000000000000-444-400000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ734-4-4444-4-440000-400004-4004i−4i004i−4i00000000004-40000004i−4i2-2002-20000002i−2i2i−2i2i−2i2i−2i0000002-22-200000000000000000000000000000000
χ744-4-4444-4-440000-400004-4004i−4i004i−4i00000000004-40000004i−4i-2200-22000000−2i2i−2i2i−2i2i−2i2i000000-22-2200000000000000000000000000000000
χ754-4-4444-4-440000-400004-4004i−4i004i−4i0000000000-44000000−4i4i2-2002-20000002i−2i2i−2i−2i2i−2i2i000000-22-2200000000000000000000000000000000
χ764-4-4444-4-440000-400004-4004i−4i004i−4i0000000000-44000000−4i4i-2200-22000000−2i2i−2i2i2i−2i2i−2i0000002-22-200000000000000000000000000000000
χ774-4-4444-4-440000-400004-400−4i4i00−4i4i00000000004-4000000−4i4i2-2002-2000000−2i2i−2i2i−2i2i−2i2i0000002-22-200000000000000000000000000000000
χ784-4-4444-4-440000-400004-400−4i4i00−4i4i00000000004-4000000−4i4i-2200-220000002i−2i2i−2i2i−2i2i−2i000000-22-2200000000000000000000000000000000
χ794-4-4444-4-440000-400004-400−4i4i00−4i4i0000000000-440000004i−4i2-2002-2000000−2i2i−2i2i2i−2i2i−2i000000-22-2200000000000000000000000000000000
χ804-4-4444-4-440000-400004-400−4i4i00−4i4i0000000000-440000004i−4i-2200-220000002i−2i2i−2i−2i2i−2i2i0000002-22-200000000000000000000000000000000
χ814-4-44-4-44440000-40000-44004i−4i00−4i4i000000004i−4i0000004-4002-200-220000002i−2i−2i2i2-2-22000000−2i2i2i−2i00000000000000000000000000000000
χ824-4-44-4-44440000-40000-44004i−4i00−4i4i000000004i−4i0000004-400-22002-2000000−2i2i2i−2i-222-20000002i−2i−2i2i00000000000000000000000000000000
χ834-4-44-4-44440000-40000-44004i−4i00−4i4i00000000−4i4i000000-44002-200-220000002i−2i−2i2i-222-20000002i−2i−2i2i00000000000000000000000000000000
χ844-4-44-4-44440000-40000-44004i−4i00−4i4i00000000−4i4i000000-4400-22002-2000000−2i2i2i−2i2-2-22000000−2i2i2i−2i00000000000000000000000000000000
χ854-4-44-4-44440000-40000-4400−4i4i004i−4i000000004i−4i000000-44002-200-22000000−2i2i2i−2i-222-2000000−2i2i2i−2i00000000000000000000000000000000
χ864-4-44-4-44440000-40000-4400−4i4i004i−4i000000004i−4i000000-4400-22002-20000002i−2i−2i2i2-2-220000002i−2i−2i2i00000000000000000000000000000000
χ874-4-44-4-44440000-40000-4400−4i4i004i−4i00000000−4i4i0000004-4002-200-22000000−2i2i2i−2i2-2-220000002i−2i−2i2i00000000000000000000000000000000
χ884-4-44-4-44440000-40000-4400−4i4i004i−4i00000000−4i4i0000004-400-22002-20000002i−2i−2i2i-222-2000000−2i2i2i−2i00000000000000000000000000000000
χ8988888888-888-8-8-8-8-888-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9088888888-8-8-888-888-8-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9188-8-88i−8i8i−8i0008-808i−8i00000000000000000000000000000000000000000000000000004ζ−4ζ4ζ3−4ζ300000000000000000000000000000000000000
χ9288-8-88i−8i8i−8i0008-808i−8i0000000000000000000000000000000000000000000000000000−4ζ4ζ−4ζ34ζ300000000000000000000000000000000000000
χ9388-8-88i−8i8i−8i000-880−8i8i00000000000000000000000000000000000000004-44i−4i00000000000000000000000000000000000000000000000000
χ9488-8-88i−8i8i−8i000-880−8i8i0000000000000000000000000000000000000000-44−4i4i00000000000000000000000000000000000000000000000000
χ9588-8-8−8i8i−8i8i0008-80−8i8i00000000000000000000000000000000000000000000000000004ζ3−4ζ34ζ−4ζ00000000000000000000000000000000000000
χ9688-8-8−8i8i−8i8i0008-80−8i8i0000000000000000000000000000000000000000000000000000−4ζ34ζ3−4ζ4ζ00000000000000000000000000000000000000
χ9788-8-8−8i8i−8i8i000-8808i−8i00000000000000000000000000000000000000004-4−4i4i00000000000000000000000000000000000000000000000000
χ9888-8-8−8i8i−8i8i000-8808i−8i0000000000000000000000000000000000000000-444i−4i00000000000000000000000000000000000000000000000000
χ998-88-88i−8i−8i8i08-8000008i−8i0000000000000000000000000000000000000000000000000000000000004ζ−4ζ4ζ3−4ζ30000000000000000000000000000
χ1008-88-88i−8i−8i8i08-8000008i−8i000000000000000000000000000000000000000000000000000000000000−4ζ4ζ−4ζ34ζ30000000000000000000000000000
χ1018-88-88i−8i−8i8i0-8800000−8i8i000000000000000000000000000000004-4004i−4i000000000000000000000000000000000000000000000000000000
χ1028-88-88i−8i−8i8i0-8800000−8i8i00000000000000000000000000000000-4400−4i4i000000000000000000000000000000000000000000000000000000
χ1038-88-8−8i8i8i−8i08-800000−8i8i0000000000000000000000000000000000000000000000000000000000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000
χ1048-88-8−8i8i8i−8i08-800000−8i8i000000000000000000000000000000000000000000000000000000000000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000
χ1058-88-8−8i8i8i−8i0-88000008i−8i000000000000000000000000000000004-400−4i4i000000000000000000000000000000000000000000000000000000
χ1068-88-8−8i8i8i−8i0-88000008i−8i00000000000000000000000000000000-44004i−4i000000000000000000000000000000000000000000000000000000
χ1078-8-8888-8-8-8000080000-888-8008-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-8888-8-8-8000080000-88-8800-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-8-888-80000800008-88-800-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-8-888-80000800008-8-88008-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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