Finite Group Databasebeta

← Group #10591153

Character table — Group #10591153

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222222244444444444444444444444444666666661212121212121212121212121212121212121212181818183636
order122244443366666612121212121212122346666666666612121212121212121212121288888888888824242424242424242424242424242424224424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-11-1-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ6111111111111111111111111-11-1-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-11-1-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-11-1-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1
χ91111-1-1-1-111111111-1-1-1-1-1-1-1-111-111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−ii−ii−iii−i−iii−i−iii−i−iii−i−i11-1-1-11
χ101111-1-1-1-111111111-1-1-1-1-1-1-1-111-111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iiii−i−iiii−i−iii−i−i−i−iii−i−iii-1-1111-1
χ111111-1-1-1-111111111-1-1-1-1-1-1-1-111-111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i−iii−i−i−iii−i−iiiii−i−iii−i−i-1-1111-1
χ121111-1-1-1-111111111-1-1-1-1-1-1-1-111-111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-1-11
χ131111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111-1-1-1-11111ii−i−iii−i−i−ii−iiii−i−i−i−iiiii−i−i−i−iii11-1-11-1
χ141111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111-1-1-1-11111ii−i−i−i−iii−iii−iii−i−i−i−iii−i−iiiii−i−i-1-111-11
χ151111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111-1-1-1-11111−i−iiiii−i−ii−i−ii−i−iiiii−i−iii−i−i−i−iii-1-111-11
χ161111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111-1-1-1-11111−i−iii−i−iiii−ii−i−i−iiiii−i−i−i−iiiii−i−i11-1-11-1
χ17222222222-122-1-12-12222-1-1-1-12-1222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100002222002200000000-1-1-1-1-1-1-1-1000000
χ18222222222-122-1-12-12222-1-1-1-12-1222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-200-2-20000000011111111000000
χ19222222222-122-1-12-12222-1-1-1-1-2-1-2-2-211-1-11111-1-2-211-1-1-1-111110000222200-2-200000000-1-1-1-11111000000
χ20222222222-122-1-12-12222-1-1-1-1-2-1-2-2-211-1-11111-1-2-211-1-1-1-111110000-2-2-2-20022000000001111-1-1-1-1000000
χ2122222222-12-1-122-12-1-1-1-122222-12-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1222200002200-1-1-1-1-1-1-1-100000000000000
χ2222222222-12-1-122-12-1-1-1-122222-12-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-20000-2-2001111111100000000000000
χ2322222222-12-1-122-12-1-1-1-12222-2-1-211-2-2-1-11111-111-2-2-1-1-1-1111122220000-2-200-1-1-1-1111100000000000000
χ2422222222-12-1-122-12-1-1-1-12222-2-1-211-2-2-1-11111-111-2-2-1-1-1-11111-2-2-2-2000022001111-1-1-1-100000000000000
χ252222-2-2-2-22-122-1-12-1-2-2-2-211112-1-222-1-1-1-1-1-1-1-1-1-2-2111111111100002i2i−2i−2i002i−2i00000000−i−iii−i−iii000000
χ262222-2-2-2-22-122-1-12-1-2-2-2-211112-1-222-1-1-1-1-1-1-1-1-1-2-211111111110000−2i−2i2i2i00−2i2i00000000ii−i−iii−i−i000000
χ272222-2-2-2-22-122-1-12-1-2-2-2-21111-2-12-2-211-1-11111-122-1-11111-1-1-1-100002i2i−2i−2i00−2i2i00000000−i−iiiii−i−i000000
χ282222-2-2-2-22-122-1-12-1-2-2-2-21111-2-12-2-211-1-11111-122-1-11111-1-1-1-10000−2i−2i2i2i002i−2i00000000ii−i−i−i−iii000000
χ292222-2-2-2-2-12-1-122-121111-2-2-2-22-1-2-1-122-1-1-1-1-1-1-111-2-2111111112i2i−2i−2i00002i−2i00−i−iii−i−iii00000000000000
χ302222-2-2-2-2-12-1-122-121111-2-2-2-22-1-2-1-122-1-1-1-1-1-1-111-2-211111111−2i−2i2i2i0000−2i2i00ii−i−iii−i−i00000000000000
χ312222-2-2-2-2-12-1-122-121111-2-2-2-2-2-1211-2-2-1-11111-1-1-1221111-1-1-1-12i2i−2i−2i0000−2i2i00−i−iiiii−i−i00000000000000
χ322222-2-2-2-2-12-1-122-121111-2-2-2-2-2-1211-2-2-1-11111-1-1-1221111-1-1-1-1−2i−2i2i2i00002i−2i00ii−i−i−i−iii00000000000000
χ3322-2-22i2i−2i−2i222-22-2-2-22i2i−2i−2i2i2i−2i−2i02000002-20000-200002i2i−2i−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000
χ3422-2-22i2i−2i−2i222-22-2-2-22i2i−2i−2i2i2i−2i−2i02000002-20000-200002i2i−2i−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000
χ3522-2-22i2i−2i−2i2-12-2-11-212i2i−2i−2i−i−iii0-1000−i3i3-11−i3−i3i3i31003−3−i−iii33−3−300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ3622-2-22i2i−2i−2i2-12-2-11-212i2i−2i−2i−i−iii0-1000−i3i3-11−i3−i3i3i31003−3−i−iii33−3−30000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ3722-2-22i2i−2i−2i2-12-2-11-212i2i−2i−2i−i−iii0-1000i3−i3-11i3i3−i3−i3100−33−i−iii−3−33300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ3822-2-22i2i−2i−2i2-12-2-11-212i2i−2i−2i−i−iii0-1000i3−i3-11i3i3−i3−i3100−33−i−iii−3−3330000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ3922-2-2−2i−2i2i2i222-22-2-2-2−2i−2i2i2i−2i−2i2i2i02000002-20000-20000−2i−2i2i2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000
χ4022-2-2−2i−2i2i2i222-22-2-2-2−2i−2i2i2i−2i−2i2i2i02000002-20000-20000−2i−2i2i2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000
χ4122-2-2−2i−2i2i2i2-12-2-11-21−2i−2i2i2iii−i−i0-1000−i3i3-11−i3−i3i3i3100−33ii−i−i−3−3330000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ4222-2-2−2i−2i2i2i2-12-2-11-21−2i−2i2i2iii−i−i0-1000−i3i3-11−i3−i3i3i3100−33ii−i−i−3−33300002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ4322-2-2−2i−2i2i2i2-12-2-11-21−2i−2i2i2iii−i−i0-1000i3−i3-11i3i3−i3−i31003−3ii−i−i33−3−30000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ4422-2-2−2i−2i2i2i2-12-2-11-21−2i−2i2i2iii−i−i0-1000i3−i3-11i3i3−i3−i31003−3ii−i−i33−3−300002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ452-22-22i−2i2i−2i22-22-22-2-22i−2i2i−2i2i−2i2i−2i0200000-220000-200002i−2i2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ462-22-22i−2i2i−2i22-22-22-2-22i−2i2i−2i2i−2i2i−2i0200000-220000-200002i−2i2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ472-22-22i−2i2i−2i-121-1-221-2−ii−ii2i−2i2i−2i0-10−i3i3001-1−i3i3−i3i313−300−ii−ii3−33−32ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000
χ482-22-22i−2i2i−2i-121-1-221-2−ii−ii2i−2i2i−2i0-10−i3i3001-1−i3i3−i3i313−300−ii−ii3−33−3−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000
χ492-22-22i−2i2i−2i-121-1-221-2−ii−ii2i−2i2i−2i0-10i3−i3001-1i3−i3i3−i31−3300−ii−ii−33−332ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000
χ502-22-22i−2i2i−2i-121-1-221-2−ii−ii2i−2i2i−2i0-10i3−i3001-1i3−i3i3−i31−3300−ii−ii−33−33−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000
χ512-22-2−2i2i−2i2i22-22-22-2-2−2i2i−2i2i−2i2i−2i2i0200000-220000-20000−2i2i−2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ522-22-2−2i2i−2i2i22-22-22-2-2−2i2i−2i2i−2i2i−2i2i0200000-220000-20000−2i2i−2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ532-22-2−2i2i−2i2i-121-1-221-2i−ii−i−2i2i−2i2i0-10−i3i3001-1−i3i3−i3i31−3300i−ii−i−33−33−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000
χ542-22-2−2i2i−2i2i-121-1-221-2i−ii−i−2i2i−2i2i0-10−i3i3001-1−i3i3−i3i31−3300i−ii−i−33−332ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000
χ552-22-2−2i2i−2i2i-121-1-221-2i−ii−i−2i2i−2i2i0-10i3−i3001-1i3−i3i3−i313−300i−ii−i3−33−3−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000
χ562-22-2−2i2i−2i2i-121-1-221-2i−ii−i−2i2i−2i2i0-10i3−i3001-1i3−i3i3−i313−300i−ii−i3−33−32ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000
χ572-2-222-2-2222-2-2-2-2222-2-222-2-220200000-2-20000200002-2-22000000000000000000000000000000002-22-200
χ582-2-222-2-2222-2-2-2-2222-2-222-2-220200000-2-20000200002-2-2200000000000000000000000000000000-22-2200
χ592-2-22-222-222-2-2-2-222-222-2-222-20200000-2-2000020000-222-2000000000000000000000000000000002-2-2200
χ602-2-22-222-222-2-2-2-222-222-2-222-20200000-2-2000020000-222-200000000000000000000000000000000-222-200
χ6144444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2414-2-2-2-21111111-2-2-2-2111111110000000000000000000000000000000000
χ6244444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-41-4222211-1-1-1-1122221111-1-1-1-10000000000000000000000000000000000
χ634444-4-4-4-4-2-2-2-2-2-2-2-22222222241-4-2-2-2-211111112222-1-1-1-1-1-1-1-10000000000000000000000000000000000
χ644444-4-4-4-4-2-2-2-2-2-2-2-222222222-414222211-1-1-1-11-2-2-2-2-1-1-1-111110000000000000000000000000000000000
χ6544-4-44i4i−4i−4i-24-224-42-4−2i−2i2i2i4i4i−4i−4i0-200000-22000020000−2i−2i2i2i00000000000000000000000000000000000000
χ6644-4-44i4i−4i−4i-2-2-22-2222−2i−2i2i2i−2i−2i2i2i01000−2i32i31-1i3i3−i3−i3-10023−23ii−i−i−3−3330000000000000000000000000000000000
χ6744-4-44i4i−4i−4i-2-2-22-2222−2i−2i2i2i−2i−2i2i2i010002i3−2i31-1−i3−i3i3i3-100−2323ii−i−i33−3−30000000000000000000000000000000000
χ6844-4-4−4i−4i4i4i-24-224-42-42i2i−2i−2i−4i−4i4i4i0-200000-220000200002i2i−2i−2i00000000000000000000000000000000000000
χ6944-4-4−4i−4i4i4i-2-2-22-22222i2i−2i−2i2i2i−2i−2i01000−2i32i31-1i3i3−i3−i3-100−2323−i−iii33−3−30000000000000000000000000000000000
χ7044-4-4−4i−4i4i4i-2-2-22-22222i2i−2i−2i2i2i−2i−2i010002i3−2i31-1−i3−i3i3i3-10023−23−i−iii−3−3330000000000000000000000000000000000
χ714-44-44i−4i4i−4i4-2-442-2-424i−4i4i−4i−2i2i−2i2i0-2000002-2000020000−2i2i−2i2i00000000000000000000000000000000000000
χ724-44-44i−4i4i−4i-2-22-22-222−2i2i−2i2i−2i2i−2i2i010−2i32i300-11i3−i3i3−i3-123−2300i−ii−i−33−330000000000000000000000000000000000
χ734-44-44i−4i4i−4i-2-22-22-222−2i2i−2i2i−2i2i−2i2i0102i3−2i300-11−i3i3−i3i3-1−232300i−ii−i3−33−30000000000000000000000000000000000
χ744-44-4−4i4i−4i4i4-2-442-2-42−4i4i−4i4i2i−2i2i−2i0-2000002-20000200002i−2i2i−2i00000000000000000000000000000000000000
χ754-44-4−4i4i−4i4i-2-22-22-2222i−2i2i−2i2i−2i2i−2i010−2i32i300-11i3−i3i3−i3-1−232300−ii−ii3−33−30000000000000000000000000000000000
χ764-44-4−4i4i−4i4i-2-22-22-2222i−2i2i−2i2i−2i2i−2i0102i3−2i300-11−i3i3−i3i3-123−2300−ii−ii−33−330000000000000000000000000000000000
χ774-4-444-4-444-2-4-4224-24-4-44-222-20-200000220000-20000-222-200000000000000000000000000000000000000
χ784-4-444-4-44-2422-4-4-24-222-24-4-440-200000220000-20000-222-200000000000000000000000000000000000000
χ794-4-444-4-44-2-22222-2-2-222-2-222-20100000-1-13-3-33100001-1-113-3-330000000000000000000000000000000000
χ804-4-444-4-44-2-22222-2-2-222-2-222-20100000-1-1-333-3100001-1-11-333-30000000000000000000000000000000000
χ814-4-44-444-44-2-4-4224-2-444-42-2-220-200000220000-200002-2-2200000000000000000000000000000000000000
χ824-4-44-444-4-2422-4-4-242-2-22-444-40-200000220000-200002-2-2200000000000000000000000000000000000000
χ834-4-44-444-4-2-22222-2-22-2-222-2-220100000-1-13-3-3310000-111-1-333-30000000000000000000000000000000000
χ844-4-44-444-4-2-22222-2-22-2-222-2-220100000-1-1-333-310000-111-13-3-330000000000000000000000000000000000

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