Finite Group Databasebeta

← Group #10591663

Character table — Group #10591663

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222222244444444444444666666668888888812121212121212121212121212121212242436363636
order124423346612121212234666661212121212128888242424246666121212124488881212121224242424242424242488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1-1-111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-11-11-1-11111-1-11111111111-11-1-1-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ611111111111111-11-11-1-11111-1-11111111111-11-1-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1
χ711111111111111-11-11-1-11111-1-111-1-1-1-1-1-1-1-1-11-1-1-11-1-11111-1-11111-1-11111-1-111-1-1
χ811111111111111-11-11-1-11111-1-111-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-11111-1-1-1-1-1-1111111-1-111
χ911-1-1-111111-1-1-1-111-1-1111-111-1-1-1-1ii−i−iii−i−i1-111-11-1-1i−ii−ii−iii−i−ii−iii−i−ii−i1-11-1
χ1011-1-1-111111-1-1-1-111-1-1111-111-1-1-1-1ii−i−iii−i−i1-111-11-1-1−iii−i−ii−i−iiii−iii−i−i−ii-11-11
χ1111-1-1-111111-1-1-1-111-1-1111-111-1-1-1-1−i−iii−i−iii1-111-11-1-1i−i−iii−iii−i−i−ii−i−iiii−i-11-11
χ1211-1-1-111111-1-1-1-111-1-1111-111-1-1-1-1−i−iii−i−iii1-111-11-1-1−ii−ii−ii−i−iii−ii−i−iii−ii1-11-1
χ1311-1-1-111111-1-1-1-1-111-1-1-11-11111-1-1ii−i−iii−i−i-1-1-1-11111i−i−ii−iiii−i−ii−i−i−iii−ii-111-1
χ1411-1-1-111111-1-1-1-1-111-1-1-11-11111-1-1ii−i−iii−i−i-1-1-1-11111−ii−iii−i−i−iiii−i−i−iiii−i1-1-11
χ1511-1-1-111111-1-1-1-1-111-1-1-11-11111-1-1−i−iii−i−iii-1-1-1-11111i−ii−i−iiii−i−i−iiii−i−i−ii1-1-11
χ1611-1-1-111111-1-1-1-1-111-1-1-11-11111-1-1−i−iii−i−iii-1-1-1-11111−iii−ii−i−i−iii−iiii−i−ii−i-111-1
χ17222222-122-122-1-12-12-1-1-1-122-1-1-1-1-12222-1-1-1-12-1-1-12-1-1-10022000000-1-1-1-1-1-1000000
χ18222222-122-122-1-12-12-1-1-1-122-1-1-1-1-1-2-2-2-211112-1-1-12-1-1-100-2-2000000111111000000
χ19222222-122-122-1-1-2-1-2-111-122-111-1-12222-1-1-1-1-2-111-2-11100-2-2000000-1-11111000000
χ20222222-122-122-1-1-2-1-2-111-122-111-1-1-2-2-2-21111-2-111-2-111002200000011-1-1-1-1000000
χ2122222-122-12-1-1222-12222-1-1-1222-1-100000000-1-1-1-1-1-1-1-1220022-1-1-1-1000000-1-10000
χ2222222-122-12-1-1222-12222-1-1-1222-1-100000000-1-1-1-1-1-1-1-1-2-200-2-21111000000110000
χ2322222-122-12-1-122-2-1-22-2-2-1-1-12-2-2-1-1000000001-1111-1112200-2-2-1-1-1-1000000110000
χ2422222-122-12-1-122-2-1-22-2-2-1-1-12-2-2-1-1000000001-1111-111-2-200221111000000-1-10000
χ252222-222-2222222020-2002-2-2-200222-22-222220-2000-2000000000000-2-20000000000
χ262222-222-2222222020-2002-2-2-20022-22-22-2-2-2-20-2000-2000000000000220000000000
χ272222-22-1-22-122-1-10-101−i3i3-1-2-21−i3i3-1-12-22-2-1-1-1-101−i3i301−i3i3000000000011−i3i3−i3i3000000
χ282222-22-1-22-122-1-10-101−i3i3-1-2-21−i3i3-1-1-22-22111101−i3i301−i3i30000000000-1-1i3−i3i3−i3000000
χ292222-22-1-22-122-1-10-101i3−i3-1-2-21i3−i3-1-12-22-2-1-1-1-101i3−i301i3−i3000000000011i3−i3i3−i3000000
χ302222-22-1-22-122-1-10-101i3−i3-1-2-21i3−i3-1-1-22-22111101i3−i301i3−i30000000000-1-1−i3i3−i3i3000000
χ3122-2-2222-222-2-2-2-202020022-2-200-2-22i−2i−2i2i2i2i−2i−2i02000-2000000000000−2i2i0000000000
χ3222-2-2222-222-2-2-2-202020022-2-200-2-2−2i2i2i−2i−2i−2i2i2i02000-20000000000002i−2i0000000000
χ3322-2-222-1-22-1-2-2110-10-1−i3i3-12-21i3−i3112i−2i−2i2i−i−iii0-1−i3i301i3−i30000000000i−i3−3−33000000
χ3422-2-222-1-22-1-2-2110-10-1−i3i3-12-21i3−i311−2i2i2i−2iii−i−i0-1−i3i301i3−i30000000000−ii−333−3000000
χ3522-2-222-1-22-1-2-2110-10-1i3−i3-12-21−i3i3112i−2i−2i2i−i−iii0-1i3−i301−i3i30000000000i−i−333−3000000
χ3622-2-222-1-22-1-2-2110-10-1i3−i3-12-21−i3i311−2i2i2i−2iii−i−i0-1i3−i301−i3i30000000000−ii3−3−33000000
χ3722-2-2-22-122-1-2-2112-1-21-1-1-1-22-111112i2i−2i−2i−i−iii21-1-1-2-111002i−2i000000−ii−i−iii000000
χ3822-2-2-22-122-1-2-2112-1-21-1-1-1-22-11111−2i−2i2i2iii−i−i21-1-1-2-11100−2i2i000000i−iii−i−i000000
χ3922-2-2-22-122-1-2-211-2-12111-1-22-1-1-1112i2i−2i−2i−i−iii-21112-1-1-100−2i2i000000−iiii−i−i000000
χ4022-2-2-22-122-1-2-211-2-12111-1-22-1-1-111−2i−2i2i2iii−i−i-21112-1-1-1002i−2i000000i−i−i−iii000000
χ4122-2-2-2-122-1211-2-22-1-2-222-11-12-2-21100000000-11-1-11-1112i−2i002i−2i−i−iii000000−ii0000
χ4222-2-2-2-122-1211-2-22-1-2-222-11-12-2-21100000000-11-1-11-111−2i2i00−2i2iii−i−i000000i−i0000
χ4322-2-2-2-122-1211-2-2-2-12-2-2-2-11-122211000000001111-1-1-1-12i−2i00−2i2i−i−iii000000i−i0000
χ4422-2-2-2-122-1211-2-2-2-12-2-2-2-11-122211000000001111-1-1-1-1−2i2i002i−2iii−i−i000000−ii0000
χ4544444-2-24-2-2-2-2-2-2414-2-2-21-2-2-2-2-21100000000-2111-21110000000000000000000000
χ4644444-2-24-2-2-2-2-2-2-41-4-2221-2-2-222110000000021-1-121-1-10000000000000000000000
χ474444-4-24-4-24-2-2440-20-400-222-400-2-200000000020002000000000000000000000000
χ484444-4-2-2-4-2-2-2-2-2-20102−2i32i31222−2i32i311000000000-1i3−i30-1i3−i30000000000000000000000
χ494444-4-2-2-4-2-2-2-2-2-201022i3−2i312222i3−2i311000000000-1−i3i30-1−i3i30000000000000000000000
χ5044-4-44-24-4-2422-4-40-20400-2-22-40022000000000-20002000000000000000000000000
χ5144-4-44-2-2-4-2-22222010-2−2i32i31-2222i3−2i3-1-10000000001i3−i30-1−i3i30000000000000000000000
χ5244-4-44-2-2-4-2-22222010-22i3−2i31-222−2i32i3-1-10000000001−i3i30-1i3−i30000000000000000000000
χ5344-4-4-4-2-24-2-2222241-42-2-212-2-222-1-100000000-2-11121-1-10000000000000000000000
χ5444-4-4-4-2-24-2-22222-41422212-2-2-2-2-1-1000000002-1-1-1-21110000000000000000000000
χ554-44i−4i0440-4-44i−4i4i−4i040000-4000004i−4i00000000000000000000000000000000000000
χ564-44i−4i04-20-424i−4i−2i2i0-20000200000−2i2i0000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000000000
χ574-44i−4i04-20-424i−4i−2i2i0-20000200000−2i2i00002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000
χ584-44i−4i0-2402-4−2i2i4i−4i0-20000200000−2i2i0000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000
χ594-44i−4i0-2402-4−2i2i4i−4i0-20000200000−2i2i0000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000
χ604-4−4i4i0440-4-4−4i4i−4i4i040000-400000−4i4i00000000000000000000000000000000000000
χ614-4−4i4i04-20-42−4i4i2i−2i0-200002000002i−2i00002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000000000
χ624-4−4i4i04-20-42−4i4i2i−2i0-200002000002i−2i0000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000000000
χ634-4−4i4i0-2402-42i−2i−4i4i0-200002000002i−2i0000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000
χ644-4−4i4i0-2402-42i−2i−4i4i0-200002000002i−2i0000000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000
χ658-88i−8i0-4-4044−4i4i−4i4i020000-2000002i−2i00000000000000000000000000000000000000
χ668-8−8i8i0-4-40444i−4i4i−4i020000-200000−2i2i00000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.