Finite Group Databasebeta

← Group #13166161

Character table — Group #13166161

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11222222244444444466666666888888888888881212121212121216161616161616161616242424242424242424242424242436363636363636484848484848108144144
order1233466121233366612121224882424242433336666121212121212466121212123366121212121212612242424242424242424242424226682424121212121212466
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-11111-1-1111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1111111-1-1-1
χ411111111111111111111-1-1-1-1-1-111111111111111-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1111
χ51111111111−1−i32−1+i321−1−i32−1+i3211111111111−1−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+i321111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−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+i321−1−i32−1+i32
χ61111111111−1−i32−1+i321−1−i32−1+i3211111111111−1−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+i32-11111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−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+i321−i321−i32-11+i321−i32
χ71111111111−1−i32−1+i321−1−i32−1+i3211111-1-1-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321-111-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11+i321−i32
χ81111111111−1−i32−1+i321−1−i32−1+i3211111-1-1-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32-11-1-1-1-1-11+i321−i321+i321+i321−i321−i321−1−i32−1+i32
χ91111111111−1+i32−1−i321−1+i32−1−i3211111111111−1+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−i321111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+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−i321−1+i32−1−i32
χ101111111111−1+i32−1−i321−1+i32−1−i3211111111111−1+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−i32-11111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+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−i321+i321+i32-11−i321+i32
χ111111111111−1+i32−1−i321−1+i32−1−i3211111-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321-111-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11−i321+i32
χ121111111111−1+i32−1−i321−1+i32−1−i3211111-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32-11-1-1-1-1-11−i321+i321−i321−i321+i321+i321−1+i32−1−i32
χ132222-222-2-2222222-2-2-2-2200000022222222-2-2-2-2-2-20-2-222002222-2-2-2-2-2-2-220000000000000000000000000000
χ142222-222-2-22−1−i3−1+i32−1−i3−1+i3-2-2-2-22000000−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3−1−i3−1+i31+i31−i31+i31+i31−i31−i30-2-22200−1−i3−1+i3−1−i3−1+i31+i31−i31+i31+i31−i31−i3-220000000000000000000000000000
χ152222-222-2-22−1+i3−1−i32−1+i3−1−i3-2-2-2-22000000−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3−1+i3−1−i31−i31+i31−i31−i31+i31+i30-2-22200−1+i3−1−i3−1+i3−1−i31−i31+i31−i31−i31+i31+i3-220000000000000000000000000000
χ16222-122-122-122-122-1-1-1220000002-12-122-1-122222222-12-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000020-1-100022-1-1-1-1000
χ17222-122-122-122-122-1-1-1220000002-12-122-1-1222222-22-12-111-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2011000-2-21111000
χ18222-122-122-1−1−i3−1+i3-1−1−i3−1+i3-1-1-122000000−1−i31+i32−1+i31−i32−1−i3−1+i31+i321−i32−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322-12-1-1-11+i321−i321+i321−i321+i321−i321+i321+i321−i321−i32-1-100000000000020-1-1000−1−i3−1+i31+i321+i321−i321−i32000
χ19222-122-122-1−1−i3−1+i3-1−1−i3−1+i3-1-1-122000000−1−i31+i32−1+i31−i32−1−i3−1+i31+i321−i32−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-22-12-1111+i321−i321+i321−i321+i321−i321+i321+i321−i321−i32-1-1000000000000-20110001+i31−i3−1−i32−1−i32−1+i32−1+i32000
χ20222-122-122-1−1+i3−1−i3-1−1+i3−1−i3-1-1-122000000−1+i31−i32−1−i31+i32−1+i3−1−i31−i321+i32−1+i3−1−i3−1+i3−1+i3−1−i3−1−i322-12-1-1-11−i321+i321−i321+i321−i321+i321−i321−i321+i321+i32-1-100000000000020-1-1000−1+i3−1−i31−i321−i321+i321+i32000
χ21222-122-122-1−1+i3−1−i3-1−1+i3−1−i3-1-1-122000000−1+i31−i32−1−i31+i32−1+i3−1−i31−i321+i32−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-22-12-1111−i321+i321−i321+i321−i321+i321−i321−i321+i321+i32-1-1000000000000-20110001−i31+i3−1+i32−1+i32−1−i32−1−i32000
χ22222-1-22-1-2-2-122-122111-220000002-12-122-1-1-2-2-2-2-2-20-212-1−i3i3-1-1-1-11111111-100000000000000−i3i300000−i3i3−i3i3000
χ23222-1-22-1-2-2-122-122111-220000002-12-122-1-1-2-2-2-2-2-20-212-1i3−i3-1-1-1-11111111-100000000000000i3−i300000i3−i3i3−i3000
χ24222-1-22-1-2-2-1−1−i3−1+i3-1−1−i3−1+i3111-22000000−1−i31+i32−1+i31−i32−1−i3−1+i31+i321−i321+i31−i31+i31+i31−i31−i30-212-1−i3i31+i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-100000000000000−i3i300000−3+i323−i323+i32−3−i32000
χ25222-1-22-1-2-2-1−1−i3−1+i3-1−1−i3−1+i3111-22000000−1−i31+i32−1+i31−i32−1−i3−1+i31+i321−i321+i31−i31+i31+i31−i31−i30-212-1i3−i31+i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-100000000000000i3−i3000003−i32−3+i32−3−i323+i32000
χ26222-1-22-1-2-2-1−1+i3−1−i3-1−1+i3−1−i3111-22000000−1+i31−i32−1−i31+i32−1+i3−1−i31−i321+i321−i31+i31−i31−i31+i31+i30-212-1−i3i31−i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-100000000000000−i3i3000003+i32−3−i32−3+i323−i32000
χ27222-1-22-1-2-2-1−1+i3−1−i3-1−1+i3−1−i3111-22000000−1+i31−i32−1−i31+i32−1+i3−1−i31−i321+i321−i31+i31−i31−i31+i31+i30-212-1i3−i31−i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-100000000000000i3−i300000−3−i323+i323−i32−3+i32000
χ2822-122-12-1-1-122-1222-1-12222-1-1-1-1-12-12-1-12222-1-1-1-10-12-1200-1-1-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-100002-1-1000000000
χ2922-122-12-1-1-122-1222-1-122-2-21111-12-12-1-12222-1-1-1-10-12-1200-1-1-1-122-1-1-1-1-1-1-2-21111-2-211110000-211000000000
χ3022-122-12-1-1-1−1−i3−1+i3-1−1−i3−1+i32-1-12222-1-1-1-11+i32−1−i31−i32−1+i31+i321−i32−1−i3−1+i3−1−i3−1+i31+i321+i321−i321−i320-12-12001+i321−i321+i321−i32−1−i3−1+i31+i321+i321−i321−i32-1-1−1−i3−1−i31+i321+i321+i321+i32−1+i3−1+i31−i321−i321−i321−i3200002-1-1000000000
χ3122-122-12-1-1-1−1−i3−1+i3-1−1−i3−1+i32-1-122-2-211111+i32−1−i31−i32−1+i31+i321−i32−1−i3−1+i3−1−i3−1+i31+i321+i321−i321−i320-12-12001+i321−i321+i321−i32−1−i3−1+i31+i321+i321−i321−i32-1-11+i31+i3−1−i32−1−i32−1−i32−1−i321−i31−i3−1+i32−1+i32−1+i32−1+i320000-211000000000
χ3222-122-12-1-1-1−1+i3−1−i3-1−1+i3−1−i32-1-12222-1-1-1-11−i32−1+i31+i32−1−i31−i321+i32−1+i3−1−i3−1+i3−1−i31−i321−i321+i321+i320-12-12001−i321+i321−i321+i32−1+i3−1−i31−i321−i321+i321+i32-1-1−1+i3−1+i31−i321−i321−i321−i32−1−i3−1−i31+i321+i321+i321+i3200002-1-1000000000
χ3322-122-12-1-1-1−1+i3−1−i3-1−1+i3−1−i32-1-122-2-211111−i32−1+i31+i32−1−i31−i321+i32−1+i3−1−i3−1+i3−1−i31−i321−i321+i321+i320-12-12001−i321+i321−i321+i32−1+i3−1−i31−i321−i321+i321+i32-1-11−i31−i3−1+i32−1+i32−1+i32−1+i321+i31+i3−1−i32−1−i32−1−i32−1−i320000-211000000000
χ3422-12-2-1211-122-122-211-220033−3−3-12-12-1-122-2-2111101-2-1200-1-1-1-1-2-211111-10033−3−30033−3−3000003−3000000000
χ3522-12-2-1211-122-122-211-2200−3−333-12-12-1-122-2-2111101-2-1200-1-1-1-1-2-211111-100−3−33300−3−33300000−33000000000
χ3622-12-2-1211-1−1−i3−1+i3-1−1−i3−1+i3-211-220033−3−31+i32−1−i31−i32−1+i31+i321−i32−1−i3−1+i31+i31−i3−1−i32−1−i32−1+i32−1+i3201-2-12001+i321−i321+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i321-1002ζ14+ζ222ζ14+ζ22−2ζ14−ζ22−2ζ14−ζ2200−ζ14−2ζ22−ζ14−2ζ22ζ14+2ζ22ζ14+2ζ22000003−3000000000
χ3722-12-2-1211-1−1−i3−1+i3-1−1−i3−1+i3-211-2200−3−3331+i32−1−i31−i32−1+i31+i321−i32−1−i3−1+i31+i31−i3−1−i32−1−i32−1+i32−1+i3201-2-12001+i321−i321+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i321-100−2ζ14−ζ22−2ζ14−ζ222ζ14+ζ222ζ14+ζ2200ζ14+2ζ22ζ14+2ζ22−ζ14−2ζ22−ζ14−2ζ2200000−33000000000
χ3822-12-2-1211-1−1+i3−1−i3-1−1+i3−1−i3-211-220033−3−31−i32−1+i31+i32−1−i31−i321+i32−1+i3−1−i31−i31+i3−1+i32−1+i32−1−i32−1−i3201-2-12001−i321+i321−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i321-100−ζ14−2ζ22−ζ14−2ζ22ζ14+2ζ22ζ14+2ζ22002ζ14+ζ222ζ14+ζ22−2ζ14−ζ22−2ζ14−ζ22000003−3000000000
χ3922-12-2-1211-1−1+i3−1−i3-1−1+i3−1−i3-211-2200−3−3331−i32−1+i31+i32−1−i31−i321+i32−1+i3−1−i31−i31+i3−1+i32−1+i32−1−i32−1−i3201-2-12001−i321+i321−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i321-100ζ14+2ζ22ζ14+2ζ22−ζ14−2ζ22−ζ14−2ζ2200−2ζ14−ζ22−2ζ14−ζ222ζ14+ζ222ζ14+ζ2200000−33000000000
χ40333333333300300333-1-1333333000000000000003-1-1-1-1330000000000-1-1000000000000-13-1-1-1-1-1000000-100
χ41333333333300300333-1-133333300000000000000-3-1-1-1-1-3-30000000000-1-10000000000001-311-1-1-1000000100
χ42333333333300300333-1-1-3-3-3-3-3-3000000000000003-1-1-1-1330000000000-1-1000000000000-1-3-1-1111000000100
χ43333333333300300333-1-1-3-3-3-3-3-300000000000000-3-1-1-1-1-3-30000000000-1-10000000000001311111000000-100
χ4444-2-24-2-2-2-2144144-21144000000-2-2-2-2-2-2-2-244-2-2-2-20-2-2-2-2001111-2-21111110000000000000000000000000000
χ4544-2-24-2-2-2-21−2−2i3−2+2i31−2−2i3−2+2i3-211440000001+i31+i31−i31−i31+i31−i31+i31−i3−2−2i3−2+2i31+i31+i31−i31−i30-2-2-2-200−1−i32−1+i32−1−i32−1+i321+i31−i3−1−i32−1−i32−1+i32−1+i32110000000000000000000000000000
χ4644-2-24-2-2-2-21−2+2i3−2−2i31−2+2i3−2−2i3-211440000001−i31−i31+i31+i31−i31+i31−i31+i3−2+2i3−2−2i31−i31−i31+i31+i30-2-2-2-200−1+i32−1−i32−1+i32−1−i321−i31+i3−1+i32−1+i32−1−i32−1−i32110000000000000000000000000000
χ4744-2-2-4-2-2221441442-1-1-44000000-2-2-2-2-2-2-2-2-4-42222022-2-200111122-1-1-1-1-110000000000000000000000000000
χ4844-2-2-4-2-2221−2−2i3−2+2i31−2−2i3−2+2i32-1-1-440000001+i31+i31−i31−i31+i31−i31+i31−i32+2i32−2i3−1−i3−1−i3−1+i3−1+i3022-2-200−1−i32−1+i32−1−i32−1+i32−1−i3−1+i31+i321+i321−i321−i32-110000000000000000000000000000
χ4944-2-2-4-2-2221−2+2i3−2−2i31−2+2i3−2−2i32-1-1-440000001−i31−i31+i31+i31−i31+i31−i31+i32−2i32+2i3−1+i3−1+i3−1−i3−1−i3022-2-200−1+i32−1−i32−1+i32−1−i32−1+i3−1−i31−i321−i321+i321+i32-110000000000000000000000000000
χ504-4440-4-4004-2-2-42200000−2i22i2−2i22i2−2i22i2-2-2-2-222220000000000000-2-22200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ514-4440-4-4004-2-2-422000002i2−2i22i2−2i22i2−2i2-2-2-2-222220000000000000-2-22200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ524-4440-4-40041+i31−i3-4−1−i3−1+i300000−2i22i2−2i22i2−2i22i21+i31+i31−i31−i3−1−i3−1+i3−1−i3−1+i300000000000001+i31−i3−1−i3−1+i300000000ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ230000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.