Finite Group Databasebeta

← Group #11923274

Character table — Group #11923274

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222444444444444444466666688888888888812121212121212161616161616161616161616161616161818242424242424242424242436363648484848
order1222344666334466666612121212121222444433666666121212122244412121212121212121212121212121212121244666666121212121244412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-11111111111111111-1-11111111111111111111-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-111111111-1-1-1-1111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1
χ4111111111111-1-111111111-1-1-1-1-1-1-1-111111111111111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1111111
χ51111111111−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111111111−1−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+i321111−1−i32−1−i32−1+i32−1+i321−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i32
χ61111111111−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111-1-1-1-111−1−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+i32-1-1111+i321+i321−i321−i3211+i321+i321−i321−i32-1-1-11+i321+i321−i321−i32
χ71111111111−1−i32−1+i32-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-1111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321−1−i32−1−i32−1+i32−1+i321-1-11+i321+i321−i321−i32
χ81111111111−1−i32−1+i32-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-1-1-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1111111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-11+i321+i321−i321−i3211+i321+i321−i321−i32-111−1−i32−1−i32−1+i32−1+i32
χ91111111111−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111111111−1+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−i321111−1+i32−1+i32−1−i32−1−i321−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i32
χ101111111111−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111-1-1-1-111−1+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−i32-1-1111−i321−i321+i321+i3211−i321−i321+i321+i32-1-1-11−i321−i321+i321+i32
χ111111111111−1+i32−1−i32-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-1111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−1+i32−1+i32−1−i32−1−i321-1-11−i321−i321+i321+i32
χ121111111111−1+i32−1−i32-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-1-1-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1111111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-11−i321−i321+i321+i3211−i321−i321+i321+i32-111−1+i32−1+i32−1−i32−1−i32
χ1311111-1-1111111-1111111-1-111-1-111-1-11111111111-1-1-1-11-11-1-1111-11-1-1-1-1-111-1-111-1-1-1-11-11111-1-1-1-1-111-11-11-1
χ1411111-1-1111111-1111111-1-111-1-1-1-1111111111111-1-1-1-11-1-11-1111-11-1-1-1-1-111-1-111-1-1111-1-1-1-1-1-11111-1-11-11-11
χ1511111-1-111111-11111111-1-1-1-11111-1-11111111111-1-1-1-1-11-11-111-11-11-1-1-1-1-1-111-1-111-1-1-111111-1-1-1-1-11-11-11-11
χ1611111-1-111111-11111111-1-1-1-111-1-1111111111111-1-1-1-1-111-1-111-11-11-1-1-1-1-1-111-1-11111-11-1-1-1-1-11111-11-11-11-1
χ1711111-1-1111−1−i32−1+i321-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-111-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-11-1-111−1−i321+i32−1+i321−i321+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-11-1−1−i32−1−i32−1+i32−1+i32-11+i321+i321−i321−i3211-1−1−i321+i32−1+i321−i32
χ1811111-1-1111−1−i32−1+i321-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-1-11-111−1−i321+i32−1+i321−i321+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32111-11+i321+i321−i321−i32-1−1−i32−1−i32−1+i32−1+i32-1-111+i32−1−i321−i32−1+i32
χ1911111-1-1111−1−i32−1+i32-11−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-11111-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-11-1111+i32−1−i321−i32−1+i321+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-1-11−1−i32−1−i32−1+i32−1+i32-11+i321+i321−i321−i321-111+i32−1−i321−i32−1+i32
χ2011111-1-1111−1−i32−1+i32-11−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-111-1-1111+i32−1−i321−i32−1+i321+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-111+i321+i321−i321−i32-1−1−i32−1−i32−1+i32−1+i32-11-1−1−i321+i32−1+i321−i32
χ2111111-1-1111−1+i32−1−i321-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-111-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-11-1-111−1+i321−i32−1−i321+i321−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-11-1−1+i32−1+i32−1−i32−1−i32-11−i321−i321+i321+i3211-1−1+i321−i32−1−i321+i32
χ2211111-1-1111−1+i32−1−i321-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-1-11-111−1+i321−i32−1−i321+i321−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32111-11−i321−i321+i321+i32-1−1+i32−1+i32−1−i32−1−i32-1-111−i32−1+i321+i32−1−i32
χ2311111-1-1111−1+i32−1−i32-11−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-11111-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11-11-1111−i32−1+i321+i32−1−i321−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-1-11−1+i32−1+i32−1−i32−1−i32-11−i321−i321+i321+i321-111−i32−1+i321+i32−1−i32
χ2411111-1-1111−1+i32−1−i32-11−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-111-1-1111−i32−1+i321+i32−1−i321−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-111−i321−i321+i321+i32-1−1+i32−1+i32−1−i32−1−i32-11-1−1+i321−i32−1−i321+i32
χ252222-122-1-1-12222222222-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1222222002-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-1-10000-100000000000
χ262222-122-1-1-122-2-2222222-1-11111000022-1-1-1-1-1-1-1-12222-2-2002-1-1-2-2-2-2-1-1-1-11111111100110000-100000000000
χ272222-122-1-1-1−1−i3−1+i322−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-1-1-1-1-10000221+i321−i321+i321−i321+i321−i321+i321−i32−1−i3−1−i3−1+i3−1+i322002-1-1−1−i3−1−i3−1+i3−1+i31+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i3200-1-10000-100000000000
χ282222-122-1-1-1−1−i3−1+i3-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-111110000221+i321−i321+i321−i321+i321−i321+i321−i32−1−i3−1−i3−1+i3−1+i3-2-2002-1-11+i31+i31−i31−i31+i321+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3200110000-100000000000
χ292222-122-1-1-1−1+i3−1−i322−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-1-1-1-1-10000221−i321+i321−i321+i321−i321+i321−i321+i32−1+i3−1+i3−1−i3−1−i322002-1-1−1+i3−1+i3−1−i3−1−i31−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i3200-1-10000-100000000000
χ302222-122-1-1-1−1+i3−1−i3-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-111110000221−i321+i321−i321+i321−i321+i321−i321+i32−1+i3−1+i3−1−i3−1−i3-2-2002-1-11−i31−i31+i31+i31−i321−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3200110000-100000000000
χ312222-1-2-2-1-1-1222-222222211-1-111000022-1-1-1-1-1-1-1-1-2-2-2-22-200-2-1-12-22-21111-1-111-1-11100-110000100000000000
χ322222-1-2-2-1-1-122-222222221111-1-1000022-1-1-1-1-1-1-1-1-2-2-2-2-2200-2-1-1-22-22111111-1-111-1-1001-10000100000000000
χ332222-1-2-2-1-1-1−1−i3−1+i32-2−1−i3−1+i3−1−i3−1+i3−1−i3−1+i311-1-1110000221+i321−i321+i321−i321+i321−i321+i321−i321+i31+i31−i31−i32-200-2-1-1−1−i31+i3−1+i31−i3−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3200-110000100000000000
χ342222-1-2-2-1-1-1−1−i3−1+i3-22−1−i3−1+i3−1−i3−1+i3−1−i3−1+i31111-1-10000221+i321−i321+i321−i321+i321−i321+i321−i321+i31+i31−i31−i3-2200-2-1-11+i3−1−i31−i3−1+i3−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32001-10000100000000000
χ352222-1-2-2-1-1-1−1+i3−1−i32-2−1+i3−1−i3−1+i3−1−i3−1+i3−1−i311-1-1110000221−i321+i321−i321+i321−i321+i321−i321+i321−i31−i31+i31+i32-200-2-1-1−1+i31−i3−1−i31+i3−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3200-110000100000000000
χ362222-1-2-2-1-1-1−1+i3−1−i3-22−1+i3−1−i3−1+i3−1−i3−1+i3−1−i31111-1-10000221−i321+i321−i321+i321−i321+i321−i321+i321−i31−i31+i31+i3-2200-2-1-11−i3−1+i31+i3−1−i3−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32001-10000100000000000
χ372-22-2200-2-222200-2-222-2-2000000002i−2i2-222-2-2-2-2220000000002-200000000000000002i−2i00000002i−2i2i−2i0000000
χ382-22-2200-2-222200-2-222-2-200000000−2i2i2-222-2-2-2-2220000000002-20000000000000000−2i2i0000000−2i2i−2i2i0000000
χ392-22-2200-2-22−1−i3−1+i3001+i31−i3−1−i3−1+i31+i31−i3000000002i−2i2-2−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i30000000002-200000000000000002i−2i00000002ζ11−2ζ112ζ7−2ζ70000000
χ402-22-2200-2-22−1−i3−1+i3001+i31−i3−1−i3−1+i31+i31−i300000000−2i2i2-2−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i30000000002-20000000000000000−2i2i0000000−2ζ112ζ11−2ζ72ζ70000000
χ412-22-2200-2-22−1+i3−1−i3001−i31+i3−1+i3−1−i31−i31+i3000000002i−2i2-2−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i30000000002-200000000000000002i−2i00000002ζ7−2ζ72ζ11−2ζ110000000
χ422-22-2200-2-22−1+i3−1−i3001−i31+i3−1+i3−1−i31−i31+i300000000−2i2i2-2−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i30000000002-20000000000000000−2i2i0000000−2ζ72ζ7−2ζ112ζ110000000
χ43333333333300330000003333333333-1-1000000000000-1-133-1-1-10000000000000000-1-1-1-10000-10000-1-1-10000
χ4433333333330033000000333333-3-3-3-3-1-1000000000000-1-1-3-3-1-1-1000000000000000011-1-10000-100001110000
χ45333333333300-3-300000033-3-3-3-33333-1-100000000000011-3-3-1-1-10000000000000000-1-1110000-10000-1110000
χ46333333333300-3-300000033-3-3-3-3-3-3-3-3-1-10000000000001133-1-1-1000000000000000011110000-100001-1-10000
χ4733333-3-3333003-3000000-3-333-3-333-3-3-1-1000000000000-113-31-1-1000000000000000011-11000010000-1-110000
χ4833333-3-3333003-3000000-3-333-3-3-3-333-1-1000000000000-11-331-1-10000000000000000-1-1-1100001000011-10000
χ4933333-3-333300-33000000-3-3-3-33333-3-3-1-10000000000001-1-331-1-10000000000000000111-1000010000-11-10000
χ5033333-3-333300-33000000-3-3-3-333-3-333-1-10000000000001-13-31-1-10000000000000000-1-11-10000100001-110000
χ5144-4-444-44-4-4-2-2002222-2-24-40000000000-2-222-2-2222-22-2000000000002-22-20000000000000000000000000000
χ5244-4-444-44-4-41+i31−i300−1−i3−1+i3−1−i3−1+i31+i31−i34-400000000001+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i3−1−i31+i3−1+i31−i300000000000−1−i31+i3−1+i31−i30000000000000000000000000000
χ5344-4-444-44-4-41−i31+i300−1+i3−1−i3−1+i3−1−i31−i31+i34-400000000001−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i3−1+i31−i3−1−i31+i300000000000−1+i31−i3−1−i31+i30000000000000000000000000000
χ5444-4-44-444-4-4-2-2002222-2-2-440000000000-2-222-2-222-22-2200000000000-22-220000000000000000000000000000
χ5544-4-44-444-4-41+i31−i300−1−i3−1+i3−1−i3−1+i31+i31−i3-4400000000001+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i31+i3−1−i31−i3−1+i3000000000001+i3−1−i31−i3−1+i30000000000000000000000000000
χ5644-4-44-444-4-41−i31+i300−1+i3−1−i3−1+i3−1−i31−i31+i3-4400000000001−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i31−i3−1+i31+i3−1−i3000000000001−i3−1+i31+i3−1−i30000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.