Finite Group Databasebeta

← Group #11923240

Character table — Group #11923240

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222444444444444444466666688888888888812121212121212161616161616161616161616161616161818242424242424242424242436363648484848
order12222236663344666666661212121244444433666666666624444121266661212121212121212121212124461212121212121212121224412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-111111111111111-1-11111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-111111111-1-1-1-1111111111111111111-11-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-11-1-1-1-1-1
χ4111111111111-1-111111111-1-1-1-111-1-1-1-1111111111111-1111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-111111
χ51111111111−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111−1−i32−1+i32−1−i32−1+i32
χ61111111111−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11111+i321+i321+i321+i321−i321−i321−i321−i32-1-1-11+i321−i321+i321−i32
χ71111111111−1−i32−1+i32-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11-1-1-111−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-11−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-11-11+i321−i321+i321−i32
χ81111111111−1−i32−1+i32-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1111-111−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-111+i321+i321+i321+i321−i321−i321−i321−i321-11−1−i32−1+i32−1−i32−1+i32
χ91111111111−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111−1+i32−1−i32−1+i32−1−i32
χ101111111111−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11111−i321−i321−i321−i321+i321+i321+i321+i32-1-1-11−i321+i321−i321+i32
χ111111111111−1+i32−1−i32-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11-1-1-111−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-11−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-11-11−i321+i321−i321+i32
χ121111111111−1+i32−1−i32-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1111-111−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-111−i321−i321−i321−i321+i321+i321+i321+i321-11−1+i32−1−i32−1+i32−1−i32
χ131111-1-11111111-1-1-111111111-1-11111-1-111-1-1-1-1111111-1-11-1111-1-1-1-1-1-11111-1-111-1-111-11-111-1-111-1-11-1-111-1-1
χ141111-1-11111111-1-1-111111111-1-111-1-11111-1-1-1-1111111-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-11-1-1-111-1-111-111-1-111
χ151111-1-1111111-11-1-1111111-1-1111111-1-111-1-1-1-11111111-1-11-111-1-1-1-111-1-1-1-111-1-111111-1-111-1-111-1-1-1-11-1-111
χ161111-1-1111111-11-1-1111111-1-11111-1-11111-1-1-1-11111111-11-1-111-1-1-1-111-1-1-1-111-1-111-1-11-1-1-1-111-1-11111-111-1-1
χ171111-1-11111−1−i32−1+i321-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-11111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11-11111+i321+i321−i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211-11-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1-1−1−i32−1+i321+i321−i32
χ181111-1-11111−1−i32−1+i321-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-111-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-111111+i321+i321−i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-1-11-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1111+i321−i32−1−i32−1+i32
χ191111-1-11111−1−i32−1+i32-11-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1111111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-11-1111+i321+i321−i321−i32−1−i32−1+i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32111-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-111+i321−i32−1−i32−1+i32
χ201111-1-11111−1−i32−1+i32-11-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11111-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-11-1-1111+i321+i321−i321−i32−1−i32−1+i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-11-1-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-1−1−i32−1+i321+i321−i32
χ211111-1-11111−1+i32−1−i321-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-11111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11-11111−i321−i321+i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211-11-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1-1−1+i32−1−i321−i321+i32
χ221111-1-11111−1+i32−1−i321-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-111-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-111111−i321−i321+i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-1-11-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1111−i321+i32−1+i32−1−i32
χ231111-1-11111−1+i32−1−i32-11-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1111111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-11-1111−i321−i321+i321+i32−1+i32−1−i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32111-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-111−i321+i32−1+i32−1−i32
χ241111-1-11111−1+i32−1−i32-11-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11111-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-11-1-1111−i321−i321+i321+i32−1+i32−1−i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-11-1-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-1−1+i32−1−i321−i321+i32
χ25222222-1-1-1-12222-1-1222222-1-1-1-1220000-1-12222-1-1-1-1-1-122002-1-1-1-1-1-12222-1-1-1-1-1-1-1-100-1-1-1000000000000000
χ26222222-1-1-1-122-2-2-1-12222221111220000-1-12222-1-1-1-1-1-1-2200-2-1-1-1-1-1-1-2-2-2-2111111110011-1000000000000000
χ27222222-1-1-1-1−1−i3−1+i322-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-1-1-12200001+i321−i32−1−i3−1−i3−1+i3−1+i31+i321−i321+i321+i321−i321−i3222002-1-11+i321+i321−i321−i32−1−i3−1+i3−1−i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i3200-1-1-1000000000000000
χ28222222-1-1-1-1−1−i3−1+i3-2-2-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i311112200001+i321−i32−1−i3−1−i3−1+i3−1+i31+i321−i321+i321+i321−i321−i32-2200-2-1-11+i321+i321−i321−i321+i31−i31+i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i320011-1000000000000000
χ29222222-1-1-1-1−1+i3−1−i322-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-1-1-12200001−i321+i32−1+i3−1+i3−1−i3−1−i31−i321+i321−i321−i321+i321+i3222002-1-11−i321−i321+i321+i32−1+i3−1−i3−1+i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i3200-1-1-1000000000000000
χ30222222-1-1-1-1−1+i3−1−i3-2-2-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1−i311112200001−i321+i32−1+i3−1+i3−1−i3−1−i31−i321+i321−i321−i321+i321+i32-2200-2-1-11−i321−i321+i321+i321−i31+i31−i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i320011-1000000000000000
χ312222-2-2-1-1-1-1222-211222222-1-111220000-1-1-2-2-2-2-1-1-1-1-1-1-2-2002-1-11111-2-222-1-111-1-111001-11000000000000000
χ322222-2-2-1-1-1-122-221122222211-1-1220000-1-1-2-2-2-2-1-1-1-1-1-12-200-2-1-1111122-2-211-1-111-1-100-111000000000000000
χ332222-2-2-1-1-1-1−1−i3−1+i32-211−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-1112200001+i321−i321+i31+i31−i31−i31+i321−i321+i321+i321−i321−i32-2-2002-1-1−1−i32−1−i32−1+i32−1+i321+i31−i3−1−i3−1+i31+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32001-11000000000000000
χ342222-2-2-1-1-1-1−1−i3−1+i3-2211−1−i3−1+i3−1−i3−1+i3−1−i3−1+i311-1-12200001+i321−i321+i31+i31−i31−i31+i321−i321+i321+i321−i321−i322-200-2-1-1−1−i32−1−i32−1+i32−1+i32−1−i3−1+i31+i31−i3−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3200-111000000000000000
χ352222-2-2-1-1-1-1−1+i3−1−i32-211−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-1112200001−i321+i321−i31−i31+i31+i31−i321+i321−i321−i321+i321+i32-2-2002-1-1−1+i32−1+i32−1−i32−1−i321−i31+i3−1+i3−1−i31−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32001-11000000000000000
χ362222-2-2-1-1-1-1−1+i3−1−i3-2211−1+i3−1−i3−1+i3−1−i3−1+i3−1−i311-1-12200001−i321+i321−i31−i31+i31+i31−i321+i321−i321−i321+i321+i322-200-2-1-1−1+i32−1+i32−1−i32−1−i32−1+i3−1−i31−i31+i3−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3200-111000000000000000
χ3722-2-2002-2-22220000-2-222-2-200002-22i−2i00220000-2-22-22-2000002-200000000000000002i−2i0002i−2i002i−2i000000000
χ3822-2-2002-2-22220000-2-222-2-200002-2−2i2i00220000-2-22-22-2000002-20000000000000000−2i2i000−2i2i00−2i2i000000000
χ3922-2-2002-2-22−1−i3−1+i300001+i31−i3−1−i3−1+i31+i31−i300002-22i−2i00−1−i3−1+i300001+i31−i3−1−i31+i3−1+i31−i3000002-200000000000000002i−2i0002ζ11−2ζ11002ζ7−2ζ7000000000
χ4022-2-2002-2-22−1−i3−1+i300001+i31−i3−1−i3−1+i31+i31−i300002-2−2i2i00−1−i3−1+i300001+i31−i3−1−i31+i3−1+i31−i3000002-20000000000000000−2i2i000−2ζ112ζ1100−2ζ72ζ7000000000
χ4122-2-2002-2-22−1+i3−1−i300001−i31+i3−1+i3−1−i31−i31+i300002-22i−2i00−1+i3−1−i300001−i31+i3−1+i31−i3−1−i31+i3000002-200000000000000002i−2i0002ζ7−2ζ7002ζ11−2ζ11000000000
χ4222-2-2002-2-22−1+i3−1−i300001−i31+i3−1+i3−1−i31−i31+i300002-2−2i2i00−1+i3−1−i300001−i31+i3−1+i31−i3−1−i31+i3000002-20000000000000000−2i2i000−2ζ72ζ700−2ζ112ζ11000000000
χ4333333333330033330000003333-1-13333000000000000-1-133-1-1-10000000000000000-1-1-1-1-100000000-1-1-10000
χ4433333333330033330000003333-1-1-3-3-3-3000000000000-1-1-3-3-1-1-1000000000000000011-1-1-1000000001110000
χ45333333333300-3-333000000-3-3-3-3-1-133330000000000001-1-3-31-1-10000000000000000-1-111-1000000001-110000
χ46333333333300-3-333000000-3-3-3-3-1-1-3-3-3-30000000000001-1331-1-100000000000000001111-100000000-11-10000
χ473333-3-33333003-3-3-300000033-3-3-1-133-3-3000000000000113-3-1-1-10000000000000000-1-11-1100000000-1110000
χ483333-3-33333003-3-3-300000033-3-3-1-1-3-33300000000000011-33-1-1-10000000000000000111-11000000001-1-10000
χ493333-3-3333300-33-3-3000000-3-333-1-133-3-3000000000000-11-331-1-10000000000000000-1-1-1110000000011-10000
χ503333-3-3333300-33-3-3000000-3-333-1-1-3-333000000000000-113-31-1-1000000000000000011-11100000000-1-110000
χ5144-4-400-222-2440000-4-444-4-400004-40000-2-2000022-22-2200000-22000000000000000000000000000000000000
χ5244-4-400-222-2−2−2i3−2+2i300002+2i32−2i3−2−2i3−2+2i32+2i32−2i300004-400001+i31−i30000−1−i3−1+i31+i3−1−i31−i3−1+i300000-22000000000000000000000000000000000000
χ5344-4-400-222-2−2+2i3−2−2i300002−2i32+2i3−2+2i3−2−2i32−2i32+2i300004-400001−i31+i30000−1+i3−1−i31−i3−1+i31+i3−1−i300000-22000000000000000000000000000000000000
χ544-44-40044-4-4-2-200002222-2-2000000004-4-2-20000222-22-20000000000000000000000000000002-2002-20000000
χ554-44-40044-4-4-2-200002222-2-200000000-44-2-20000222-22-2000000000000000000000000000000-2200-220000000
χ564-44-40044-4-41+i31−i30000−1−i3−1+i3−1−i3−1+i31+i31−i3000000004-41+i31−i30000−1−i3−1+i3−1−i31+i3−1+i31−i3000000000000000000000000000000−1−i31+i300−1+i31−i30000000
χ574-44-40044-4-41+i31−i30000−1−i3−1+i3−1−i3−1+i31+i31−i300000000-441+i31−i30000−1−i3−1+i3−1−i31+i3−1+i31−i30000000000000000000000000000001+i3−1−i3001−i3−1+i30000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.