Finite Group Databasebeta

← Group #11923257

Character table — Group #11923257

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222444444444444444466666688888888888812121212121212161616161616161616161616161616161818242424242424242424242436363648484848
order1222223666233466666666661212444444336666666666444441212666666666612121212121244121212121212121212121224412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-111111111111111-11-1111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111−1−i32−1+i3211111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211111111−1−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
χ411111111111−1−i32−1+i3211111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211-11-111−1−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
χ511111111111−1+i32−1−i3211111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211111111−1+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
χ611111111111−1+i32−1−i3211111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211-11-111−1+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
χ71111111111-111-111-1-1111111-1-11111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111-11-111111111-1-11-1-1-1-1
χ81111111111-111-111-1-1111111-1-111-1-1-1-11111111111111-11-1111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-111-11111
χ91111111111-1−1−i32−1+i32-111-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-1-1-1-1111+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321−i321+i321+i321−i321−i3211-11-1−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-111+i321+i321−i321−i32
χ101111111111-1−1−i32−1+i32-111-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-11-11111+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321−i321+i321+i321−i321−i32-1-1-11-11+i321+i321+i321+i321−i321−i321−i321−i3211-1−1−i32−1−i32−1+i32−1+i32
χ111111111111-1−1+i32−1−i32-111-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-1-1-1-1111−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321+i321−i321−i321+i321+i3211-11-1−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-111−i321−i321+i321+i32
χ121111111111-1−1+i32−1−i32-111-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-11-11111−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321+i321−i321−i321+i321+i32-1-1-11-11−i321−i321−i321−i321+i321+i321+i321+i3211-1−1+i32−1+i32−1−i32−1−i32
χ131111-1-11111111-1-1-111111111-1-11111-1-111-1-1-1-1111111-111-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-1111-1-111-1-11-111-11-1
χ141111-1-11111111-1-1-111111111-1-111-1-11111-1-1-1-1111111-11-1-111111-1-111-1-111-1-1-1-1-1-111-1-11-1-111-1-111-11-1-11-11
χ151111-1-111111−1−i32−1+i32-1-1-111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-11111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-111-1-111−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321−i321+i321+i321−i321−i32-1-1-1-11−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-11−1−i321+i32−1+i321−i32
χ161111-1-111111−1−i32−1+i32-1-1-111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-111-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-11-1-1111−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321−i321+i321+i321−i321−i3211-1-111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-11-11+i32−1−i321−i32−1+i32
χ171111-1-111111−1+i32−1−i32-1-1-111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-11111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-111-1-111−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321+i321−i321−i321+i321+i32-1-1-1-11−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-11−1+i321−i32−1−i321+i32
χ181111-1-111111−1+i32−1−i32-1-1-111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-111-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-11-1-1111−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321+i321−i321−i321+i321+i3211-1-111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-11-11−i32−1+i321+i32−1−i32
χ191111-1-11111-1111-1-1-1-1111111111111-1-111-1-1-1-1111111-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11-1-111-1-111-1-1-111-11-11
χ201111-1-11111-1111-1-1-1-11111111111-1-11111-1-1-1-1111111-1-111-111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1111-1-11-11-1
χ211111-1-11111-1−1−i32−1+i321-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111-1-1−1−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+i321−i321−i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1111+i32−1−i321−i32−1+i32
χ221111-1-11111-1−1−i32−1+i321-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-111-1111+i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111-1-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-1-1−1−i321+i32−1+i321−i32
χ231111-1-11111-1−1+i32−1−i321-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111-1-1−1+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−i321+i321+i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1111−i32−1+i321+i32−1−i32
χ241111-1-11111-1−1+i32−1−i321-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-111-1111−i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111-1-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-1-1−1+i321−i32−1−i321+i32
χ25222222-1-1-1-12222-1-1-1-1222222-1-1220000-1-12222-1-1-1-1-1-122020-1-122-1-1-1-1-1-1-1-122-1-1-1-100-1-1-1000000000000000
χ26222222-1-1-1-12−1−i3−1+i32-1-1-1-1−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3-1-12200001+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321−i321−i321+i321−i3222020-1-1−1−i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i32−1−i3−1+i31+i321+i321−i321−i3200-1-1-1000000000000000
χ27222222-1-1-1-12−1+i3−1−i32-1-1-1-1−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3-1-12200001−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321+i321+i321−i321+i3222020-1-1−1+i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i32−1+i3−1−i31−i321−i321+i321+i3200-1-1-1000000000000000
χ28222222-1-1-1-1-222-2-1-11122222211220000-1-12222-1-1-1-1-1-12-20-20-1-1-2-2-1-111-1-111-2-21111001-11000000000000000
χ29222222-1-1-1-1-2−1−i3−1+i3-2-1-111−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3112200001+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321−i321−i321+i321−i322-20-20-1-11+i31−i31+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i31−i3−1−i32−1−i32−1+i32−1+i32001-11000000000000000
χ30222222-1-1-1-1-2−1+i3−1−i3-2-1-111−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3112200001−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321+i321+i321−i321+i322-20-20-1-11−i31+i31−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i31+i3−1+i32−1+i32−1−i32−1−i32001-11000000000000000
χ312222-2-2-1-1-1-1222-211-1-122222211220000-1-1-2-2-2-2-1-1-1-1-1-1-220-20-1-12211-1-111-1-1-2-211110011-1000000000000000
χ322222-2-2-1-1-1-12−1−i3−1+i3-211-1-1−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3112200001+i321−i321+i31+i31−i31−i31+i321+i321−i321−i321+i321−i32-220-20-1-1−1−i3−1+i3−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i320011-1000000000000000
χ332222-2-2-1-1-1-12−1+i3−1−i3-211-1-1−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3112200001−i321+i321−i31−i31+i31+i31−i321−i321+i321+i321−i321+i32-220-20-1-1−1+i3−1−i3−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i320011-1000000000000000
χ342222-2-2-1-1-1-1-22221111222222-1-1220000-1-1-2-2-2-2-1-1-1-1-1-1-2-2020-1-1-2-21111111122-1-1-1-100-111000000000000000
χ352222-2-2-1-1-1-1-2−1−i3−1+i321111−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3-1-12200001+i321−i321+i31+i31−i31−i31+i321+i321−i321−i321+i321−i32-2-2020-1-11+i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i3−1+i31+i321+i321−i321−i3200-111000000000000000
χ362222-2-2-1-1-1-1-2−1+i3−1−i321111−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3-1-12200001−i321+i321−i31−i31+i31+i31−i321−i321+i321+i321−i321+i32-2-2020-1-11−i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i3−1−i31−i321−i321+i321+i3200-111000000000000000
χ3722-2-2002-2-22022000002-22-2-2-2002-2002i−2i2200002-22-2-2-2000002-200000000000000002i−2i000002i−2i002i−2i0000000
χ3822-2-2002-2-22022000002-22-2-2-2002-200−2i2i2200002-22-2-2-2000002-20000000000000000−2i2i00000−2i2i00−2i2i0000000
χ3922-2-2002-2-220−1−i3−1+i300000−1−i31+i3−1+i31−i31+i31−i3002-2002i−2i−1−i3−1+i30000−1−i31+i3−1+i31−i31+i31−i3000002-200000000000000002i−2i000002ζ11−2ζ11002ζ7−2ζ70000000
χ4022-2-2002-2-220−1−i3−1+i300000−1−i31+i3−1+i31−i31+i31−i3002-200−2i2i−1−i3−1+i30000−1−i31+i3−1+i31−i31+i31−i3000002-20000000000000000−2i2i00000−2ζ112ζ1100−2ζ72ζ70000000
χ4122-2-2002-2-220−1+i3−1−i300000−1+i31−i3−1−i31+i31−i31+i3002-2002i−2i−1+i3−1−i30000−1+i31−i3−1−i31+i31−i31+i3000002-200000000000000002i−2i000002ζ7−2ζ7002ζ11−2ζ110000000
χ4222-2-2002-2-220−1+i3−1−i300000−1+i31−i3−1−i31+i31−i31+i3002-200−2i2i−1+i3−1−i30000−1+i31−i3−1−i31+i31−i31+i3000002-20000000000000000−2i2i00000−2ζ72ζ700−2ζ112ζ110000000
χ4333333333333003333300000033-1-13333000000000000-1-13-13-1-10000000000000000-1-1-1-1-100000000-1-1-10000
χ4433333333333003333300000033-1-1-3-3-3-3000000000000-1-1-3-1-3-1-1000000000000000011-1-1-1000000001110000
χ453333333333-300-333-3-3000000-3-3-1-13333000000000000-11-31-3-1-10000000000000000-1-11-110000000011-10000
χ463333333333-300-333-3-3000000-3-3-1-1-3-3-3-3000000000000-11313-1-10000000000000000111-1100000000-1-110000
χ473333-3-33333300-3-3-333000000-3-3-1-133-3-30000000000001-131-3-1-100000000000000001111-100000000-11-10000
χ483333-3-33333300-3-3-333000000-3-3-1-1-3-3330000000000001-1-313-1-10000000000000000-1-111-1000000001-110000
χ493333-3-33333-3003-3-3-3-300000033-1-133-3-300000000000011-3-13-1-1000000000000000011-111000000001-1-10000
χ503333-3-33333-3003-3-3-3-300000033-1-1-3-333000000000000113-1-3-1-10000000000000000-1-1-11100000000-1110000
χ5144-4-400-222-2044000004-44-4-4-4004-40000-2-20000-22-222200000-22000000000000000000000000000000000000
χ5244-4-400-222-20−2−2i3−2+2i300000−2−2i32+2i3−2+2i32−2i32+2i32−2i3004-400001+i31−i300001+i3−1−i31−i3−1+i3−1−i3−1+i300000-22000000000000000000000000000000000000
χ5344-4-400-222-20−2+2i3−2−2i300000−2+2i32−2i3−2−2i32+2i32−2i32+2i3004-400001−i31+i300001−i3−1+i31+i3−1−i3−1+i3−1−i300000-22000000000000000000000000000000000000
χ544-44-44-444-4-40-2-204-4002222-2-200000000-2-22-22-22222-2-20000000002-2002-20000000000000000000000000000
χ554-44-44-444-4-401+i31−i304-400−1−i3−1−i3−1+i3−1+i31+i31−i3000000001+i31−i3−1−i31+i3−1+i31−i3−1−i3−1−i3−1+i3−1+i31+i31−i3000000000−1−i31+i300−1+i31−i30000000000000000000000000000
χ564-44-44-444-4-401−i31+i304-400−1+i3−1+i3−1−i3−1−i31−i31+i3000000001−i31+i3−1+i31−i3−1−i31+i3−1+i3−1+i3−1−i3−1−i31−i31+i3000000000−1+i31−i300−1−i31+i30000000000000000000000000000
χ574-44-44-4-2-2220-2-20-22−2i32i32222-2-2−2i32i3000000112-22-2-1-1-1-111000000000-11−i3i3-11−i3i300−i3i3−i3i300000000000000000000
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χ871212-12-1200-666-60000000000000000-440000000000000000000002-2000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.