Finite Group Databasebeta

← Group #11923241

Character table — Group #11923241

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222444444444444444466666688888888888812121212121212161616161616161616161616161616161818242424242424242424242436363648484848
order12223446662334666666661212121244444433666666121212122244412126666661212121212121212121244612121212121212121212444661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-11111111111111-11-11111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111−1−i32−1+i32111−1−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
χ411111111111−1−i32−1+i32111−1−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+i321-11-1111−1−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
χ511111111111−1+i32−1−i32111−1+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
χ611111111111−1+i32−1−i32111−1+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−i321-11-1111−1+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
χ71111111111-111-1-1-1111111-1-1111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1111-1-111111111-11-1-1-1-1-1
χ81111111111-111-1-1-1111111-1-11111-1-1-1-111111111111111-11-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-11-111111
χ91111111111-1−1−i32−1+i32-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111111111−1−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−i321+i321+i321−i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32111-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-11-11+i321−i321+i321−i32
χ101111111111-1−1−i32−1+i32-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211-11-1111+i321−i321+i321+i321−i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-11-1-11+i321+i321−i321−i321+i321+i321−i321−i321-11−1−i32−1+i32−1−i32−1+i32
χ111111111111-1−1+i32−1−i32-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111111111−1+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+i321−i321−i321+i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32111-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-11-11−i321+i321−i321+i32
χ121111111111-1−1+i32−1−i32-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211-11-1111−i321+i321−i321−i321+i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-11-1-11−i321−i321+i321+i321−i321−i321+i321+i321-11−1+i32−1−i32−1+i32−1−i32
χ1311111-1-1111111-111111111-1-1-1-11111-1-111111111-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-111-1-1
χ1411111-1-1111111-111111111-1-1-1-111-1-11111111111-1-1-1-1-1-111-111111111-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-1-11-1-111
χ1511111-1-11111−1−i32−1+i32-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-11111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-111-1-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i3211-1−1−i32−1+i321+i321−i32
χ1611111-1-11111−1−i32−1+i32-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-111-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-111-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-11−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-111+i321−i32−1−i32−1+i32
χ1711111-1-11111−1+i32−1−i32-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-11111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-111-1-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i3211-1−1+i32−1−i321−i321+i32
χ1811111-1-11111−1+i32−1−i32-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-111-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-111-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-11−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-111−i321+i32−1+i32−1−i32
χ1911111-1-1111-1111-1-111111111-1-11111-1-111111111-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-11-1-1-1-1-11111-111-1-111
χ2011111-1-1111-1111-1-111111111-1-111-1-11111111111-1-1-1-1-11-1-1111-1-1-1-1-1-111-1-111-1-11111-11-11111-1-1-1-11-1-111-1-1
χ2111111-1-1111-1−1−i32−1+i321-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-11111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-1-111111+i321−i321+i321+i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-1-11-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1111+i321−i32−1−i32−1+i32
χ2211111-1-1111-1−1−i32−1+i321-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-111-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-11-1-11111+i321−i321+i321+i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-11-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321-1-1−1−i32−1+i321+i321−i32
χ2311111-1-1111-1−1+i32−1−i321-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-11111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-1-111111−i321+i321−i321−i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-1-11-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1111−i321+i32−1+i32−1−i32
χ2411111-1-1111-1−1+i32−1−i321-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-111-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-11-1-11111−i321+i321−i321−i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-11-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321-1-1−1+i32−1−i321−i321+i32
χ252222-122-1-1-12222-1-1222222-1-1-1-1220000-1-1-1-1-1-1-1-1222220202-1-122-1-1-1-122-1-1-1-1-1-1-1-100-1-1-1000000000000000
χ262222-122-1-1-12−1−i3−1+i32-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-1-1-12200001+i321−i321+i321−i321+i321+i321−i321−i32−1−i3−1−i3−1+i3−1+i320202-1-1−1−i3−1+i31+i321+i321−i321−i32−1−i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i3200-1-1-1000000000000000
χ272222-122-1-1-12−1+i3−1−i32-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-1-1-12200001−i321+i321−i321+i321−i321−i321+i321+i32−1+i3−1+i3−1−i3−1−i320202-1-1−1+i3−1−i31−i321−i321+i321+i32−1+i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i3200-1-1-1000000000000000
χ282222-122-1-1-1-222-21122222211-1-1220000-1-1-1-1-1-1-1-1222220-20-2-1-1-2-21111-2-2-1-111-1-11100-111000000000000000
χ292222-122-1-1-1-2−1−i3−1+i3-211−1−i3−1+i3−1−i3−1+i3−1−i3−1+i311-1-12200001+i321−i321+i321−i321+i321+i321−i321−i32−1−i3−1−i3−1+i3−1+i320-20-2-1-11+i31−i3−1−i32−1−i32−1+i32−1+i321+i31−i31+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3200-111000000000000000
χ302222-122-1-1-1-2−1+i3−1−i3-211−1+i3−1−i3−1+i3−1−i3−1+i3−1−i311-1-12200001−i321+i321−i321+i321−i321−i321+i321+i32−1+i3−1+i3−1−i3−1−i320-20-2-1-11−i31+i3−1+i32−1+i32−1−i32−1−i321−i31+i31−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3200-111000000000000000
χ312222-1-2-2-1-1-1222-2-1-12222221111220000-1-1-1-1-1-1-1-1-2-2-2-2-2020-2-1-122-1-1-1-1-2-2111111110011-1000000000000000
χ322222-1-2-2-1-1-12−1−i3−1+i3-2-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i311112200001+i321−i321+i321−i321+i321+i321−i321−i321+i31+i31−i31−i3-2020-2-1-1−1−i3−1+i31+i321+i321−i321−i321+i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i320011-1000000000000000
χ332222-1-2-2-1-1-12−1+i3−1−i3-2-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1−i311112200001−i321+i321−i321+i321−i321−i321+i321+i321−i31−i31+i31+i3-2020-2-1-1−1+i3−1−i31−i321−i321+i321+i321−i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i320011-1000000000000000
χ342222-1-2-2-1-1-1-222211222222-1-111220000-1-1-1-1-1-1-1-1-2-2-2-2-20-202-1-1-2-211112211-1-111-1-1001-11000000000000000
χ352222-1-2-2-1-1-1-2−1−i3−1+i3211−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-1112200001+i321−i321+i321−i321+i321+i321−i321−i321+i31+i31−i31−i3-20-202-1-11+i31−i3−1−i32−1−i32−1+i32−1+i32−1−i3−1+i3−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32001-11000000000000000
χ362222-1-2-2-1-1-1-2−1+i3−1−i3211−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-1112200001−i321+i321−i321+i321−i321−i321+i321+i321−i31−i31+i31+i3-20-202-1-11−i31+i3−1+i32−1+i32−1−i32−1−i32−1+i3−1−i3−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32001-11000000000000000
χ3722-2-2200-2-2202200022-2-2-2-200002-2002i−2i22-2-22-22-20000000002-200000000000000002i−2i0002i−2i2i−2i00000000000
χ3822-2-2200-2-2202200022-2-2-2-200002-200−2i2i22-2-22-22-20000000002-20000000000000000−2i2i000−2i2i−2i2i00000000000
χ3922-2-2200-2-220−1−i3−1+i3000−1−i3−1+i31+i31−i31+i31−i300002-2002i−2i−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i30000000002-200000000000000002i−2i0002ζ11−2ζ112ζ7−2ζ700000000000
χ4022-2-2200-2-220−1−i3−1+i3000−1−i3−1+i31+i31−i31+i31−i300002-200−2i2i−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i30000000002-20000000000000000−2i2i000−2ζ112ζ11−2ζ72ζ700000000000
χ4122-2-2200-2-220−1+i3−1−i3000−1+i3−1−i31−i31+i31−i31+i300002-2002i−2i−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i30000000002-200000000000000002i−2i0002ζ7−2ζ72ζ11−2ζ1100000000000
χ4222-2-2200-2-220−1+i3−1−i3000−1+i3−1−i31−i31+i31−i31+i300002-200−2i2i−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i30000000002-20000000000000000−2i2i000−2ζ72ζ7−2ζ112ζ1100000000000
χ4333333333333003330000003333-1-13333000000000000-13-13-1-1-10000000000000000-1-1-1-1-100000000-1-1-10000
χ4433333333333003330000003333-1-1-3-3-3-3000000000000-1-3-1-3-1-1-1000000000000000011-1-1-1000000001110000
χ453333333333-300-3-3-3000000-3-333-1-13333000000000000-1-31-31-1-10000000000000000-1-1-111000000001-110000
χ463333333333-300-3-3-3000000-3-333-1-1-3-3-3-3000000000000-13131-1-1000000000000000011-11100000000-11-10000
χ4733333-3-3333300-333000000-3-3-3-3-1-133-3-300000000000013-1-31-1-100000000000000001111-100000000-1-110000
χ4833333-3-3333300-333000000-3-3-3-3-1-1-3-3330000000000001-3-131-1-10000000000000000-1-111-10000000011-10000
χ4933333-3-3333-3003-3-300000033-3-3-1-133-3-30000000000001-313-1-1-10000000000000000111-11000000001-1-10000
χ5033333-3-3333-3003-3-300000033-3-3-1-1-3-333000000000000131-3-1-1-10000000000000000-1-11-1100000000-1110000
χ5144-4-4-20022-204400044-4-4-4-400004-40000-2-222-22-22000000000-22000000000000000000000000000000000000
χ5244-4-4-20022-20−2−2i3−2+2i3000−2−2i3−2+2i32+2i32−2i32+2i32−2i300004-400001+i31−i3−1−i3−1+i31+i3−1−i31−i3−1+i3000000000-22000000000000000000000000000000000000
χ5344-4-4-20022-20−2+2i3−2−2i3000−2+2i3−2−2i32−2i32+2i32−2i32+2i300004-400001−i31+i3−1+i3−1−i31−i3−1+i31+i3−1−i3000000000-22000000000000000000000000000000000000
χ544-44-44004-4-40-2-20002222-2-20000004-400-2-2222-22-20000000000000000000000000000000000002-22-20000000
χ554-44-44004-4-40-2-20002222-2-2000000-4400-2-2222-22-2000000000000000000000000000000000000-22-220000000
χ564-44-44004-4-401+i31−i3000−1−i3−1+i3−1−i3−1+i31+i31−i30000004-4001+i31−i3−1−i3−1+i3−1−i31+i3−1+i31−i3000000000000000000000000000000000000−1−i31+i3−1+i31−i30000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.