Finite Group Databasebeta

← Group #10591156

Character table — Group #10591156

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222222244444444444444444444444444666666661212121212121212121212121212121212121212181818183636
order1222444433666666121212121212121223466666666666121212121212121212121212444488882466881212121212122424242424242424888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1
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
χ5111111111111111111111111-11-1-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ6111111111111111111111111-11-1-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-11-1-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-11-1-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1
χ91111-1-1-1-111111111-1-1-1-1-1-1-1-111-111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−i1-111i−i11-1-1-1-1ii−i−iii−i−iii−i−ii−i
χ101111-1-1-1-111111111-1-1-1-1-1-1-1-111-111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iii1-111−ii11-1-1-1-1−i−iii−i−iii−i−iii−ii
χ111111-1-1-1-111111111-1-1-1-1-1-1-1-111-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i-11-1-1i−i-1-11111ii−i−iii−i−i−i−iii−ii
χ121111-1-1-1-111111111-1-1-1-1-1-1-1-111-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii-11-1-1−ii-1-11111−i−iii−i−iiiii−i−ii−i
χ131111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111-1-1-1-1111111-1-1ii−i−i-11-1-1−ii11-1-111ii−i−i−i−iiiii−i−i−ii
χ141111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111-1-1-1-1111111-1-1−i−iii-11-1-1i−i11-1-111−i−iiiii−i−i−i−iiii−i
χ151111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111-1-1-1-11111-1-111ii−i−i1-111−ii-1-111-1-1ii−i−i−i−iii−i−iiii−i
χ161111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111-1-1-1-11111-1-111−i−iii1-111i−i-1-111-1-1−i−iiiii−i−iii−i−i−ii
χ17222222222-1222-1-1-122-1-1-1-1222-1222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222000022-1-100-1-1-1-1-1-100000000000000
χ18222222222-1222-1-1-122-1-1-1-1222-1222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-2110011111100000000000000
χ19222222222-1222-1-1-122-1-1-1-122-2-1-2-2-211-1-11111-1-2-211-1-1-1-1111122220000-2-21100-1-1-1-11100000000000000
χ20222222222-1222-1-1-122-1-1-1-122-2-1-2-2-211-1-11111-1-2-211-1-1-1-11111-2-2-2-2000022-1-1001111-1-100000000000000
χ2122222222-12-1-1-1222-1-12222-1-12-12-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100002222000022000000-1-1-1-1-1-1-1-1000000
χ2222222222-12-1-1-1222-1-12222-1-12-12-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-20000-2-200000011111111000000
χ2322222222-12-1-1-1222-1-12222-1-1-2-1-211-2-2-1-11111-111-2-2-1-1-1-11111000022220000-2-2000000-1-1-1-11111000000
χ2422222222-12-1-1-1222-1-12222-1-1-2-1-211-2-2-1-11111-111-2-2-1-1-1-111110000-2-2-2-20000220000001111-1-1-1-1000000
χ252222-2-2-2-22-1222-1-1-1-2-21111-2-22-1-222-1-1-1-1-1-1-1-1-1-2-2111111111122-2-200002-2-1-100-1-1111100000000000000
χ262222-2-2-2-22-1222-1-1-1-2-21111-2-22-1-222-1-1-1-1-1-1-1-1-1-2-21111111111-2-2220000-22110011-1-1-1-100000000000000
χ272222-2-2-2-22-1222-1-1-1-2-21111-2-2-2-12-2-211-1-11111-122-1-11111-1-1-1-122-2-20000-221100-1-111-1-100000000000000
χ282222-2-2-2-22-1222-1-1-1-2-21111-2-2-2-12-2-211-1-11111-122-1-11111-1-1-1-1-2-22200002-2-1-10011-1-11100000000000000
χ292222-2-2-2-2-12-1-1-122211-2-2-2-2112-1-2-1-122-1-1-1-1-1-1-111-2-21111111100002i2i−2i−2i00002i−2i000000−i−iii−i−iii000000
χ302222-2-2-2-2-12-1-1-122211-2-2-2-2112-1-2-1-122-1-1-1-1-1-1-111-2-2111111110000−2i−2i2i2i0000−2i2i000000ii−i−iii−i−i000000
χ312222-2-2-2-2-12-1-1-122211-2-2-2-211-2-1211-2-2-1-11111-1-1-1221111-1-1-1-100002i2i−2i−2i0000−2i2i000000−i−iiiii−i−i000000
χ322222-2-2-2-2-12-1-1-122211-2-2-2-211-2-1211-2-2-1-11111-1-1-1221111-1-1-1-10000−2i−2i2i2i00002i−2i000000ii−i−i−i−iii000000
χ3322-2-22i−2i2i−2i222-2-22-2-22i−2i2i2i−2i−2i2i−2i02000002-20000-200002i2i−2i−2i00000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ3422-2-22i−2i2i−2i222-2-22-2-22i−2i2i2i−2i−2i2i−2i02000002-20000-200002i2i−2i−2i000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ3522-2-2−2i2i−2i2i222-2-22-2-2−2i2i−2i−2i2i2i−2i2i02000002-20000-20000−2i−2i2i2i000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ3622-2-2−2i2i−2i2i222-2-22-2-2−2i2i−2i−2i2i2i−2i2i02000002-20000-20000−2i−2i2i2i00000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ372-22-22i−2i−2i2i22-22-2-22-22i−2i2i−2i2i−2i−2i2i0200000-220000-200002i−2i2i−2i00002-22i−2i00000000002-22i−2i0000000000000000
χ382-22-22i−2i−2i2i22-22-2-22-22i−2i2i−2i2i−2i−2i2i0200000-220000-200002i−2i2i−2i0000-22−2i2i0000000000-22−2i2i0000000000000000
χ392-22-22i−2i−2i2i2-1-22-21-112i−2i−ii−ii−2i2i0-1000−i3i31-1−i3−i3i3i31003−3−ii−ii33−3−32-22i−2i000000−i3i300-11−ii3−300000000000000
χ402-22-22i−2i−2i2i2-1-22-21-112i−2i−ii−ii−2i2i0-1000−i3i31-1−i3−i3i3i31003−3−ii−ii33−3−3-22−2i2i000000i3−i3001-1i−i−3300000000000000
χ412-22-22i−2i−2i2i2-1-22-21-112i−2i−ii−ii−2i2i0-1000i3−i31-1i3i3−i3−i3100−33−ii−ii−3−3332-22i−2i000000i3−i300-11−ii−3300000000000000
χ422-22-22i−2i−2i2i2-1-22-21-112i−2i−ii−ii−2i2i0-1000i3−i31-1i3i3−i3−i3100−33−ii−ii−3−333-22−2i2i000000−i3i3001-1i−i3−300000000000000
χ432-22-2−2i2i2i−2i22-22-2-22-2−2i2i−2i2i−2i2i2i−2i0200000-220000-20000−2i2i−2i2i00002-2−2i2i00000000002-2−2i2i0000000000000000
χ442-22-2−2i2i2i−2i22-22-2-22-2−2i2i−2i2i−2i2i2i−2i0200000-220000-20000−2i2i−2i2i0000-222i−2i0000000000-222i−2i0000000000000000
χ452-22-2−2i2i2i−2i2-1-22-21-11−2i2ii−ii−i2i−2i0-1000−i3i31-1−i3−i3i3i3100−33i−ii−i−3−3332-2−2i2i000000−i3i300-11i−i−3300000000000000
χ462-22-2−2i2i2i−2i2-1-22-21-11−2i2ii−ii−i2i−2i0-1000−i3i31-1−i3−i3i3i3100−33i−ii−i−3−333-222i−2i000000i3−i3001-1−ii3−300000000000000
χ472-22-2−2i2i2i−2i2-1-22-21-11−2i2ii−ii−i2i−2i0-1000i3−i31-1i3i3−i3−i31003−3i−ii−i33−3−32-2−2i2i000000i3−i300-11i−i3−300000000000000
χ482-22-2−2i2i2i−2i2-1-22-21-11−2i2ii−ii−i2i−2i0-1000i3−i31-1i3i3−i3−i31003−3i−ii−i33−3−3-222i−2i000000−i3i3001-1−ii−3300000000000000
χ492-2-2222-2-222-2-22-2-22222-2-22-2-20200000-2-20000200002-2-22000000002i−2i2i−2i0000000000002i−2i2i−2i0000000000
χ502-2-2222-2-222-2-22-2-22222-2-22-2-20200000-2-20000200002-2-2200000000−2i2i−2i2i000000000000−2i2i−2i2i0000000000
χ512-2-2222-2-2-1211-1-2-22-1-12-2-22110-10−i3i30011−i3i3−i3i3-1−i3i300-111-1−i3i3−i3i300002i−2i2i−2i000000000000−ii−ii3−33−3000000
χ522-2-2222-2-2-1211-1-2-22-1-12-2-22110-10−i3i30011−i3i3−i3i3-1−i3i300-111-1−i3i3−i3i30000−2i2i−2i2i000000000000i−ii−i−33−33000000
χ532-2-2222-2-2-1211-1-2-22-1-12-2-22110-10i3−i30011i3−i3i3−i3-1i3−i300-111-1i3−i3i3−i300002i−2i2i−2i000000000000−ii−ii−33−33000000
χ542-2-2222-2-2-1211-1-2-22-1-12-2-22110-10i3−i30011i3−i3i3−i3-1i3−i300-111-1i3−i3i3−i30000−2i2i−2i2i000000000000i−ii−i3−33−3000000
χ552-2-22-2-22222-2-22-2-22-2-2-222-2220200000-2-2000020000-222-2000000002-2-220000000000002-2-220000000000
χ562-2-22-2-22222-2-22-2-22-2-2-222-2220200000-2-2000020000-222-200000000-222-2000000000000-222-20000000000
χ572-2-22-2-222-1211-1-2-2211-222-2-1-10-10−i3i30011−i3i3−i3i3-1i3−i3001-1-11i3−i3i3−i300002-2-22000000000000-111-1−i3i3i3−i3000000
χ582-2-22-2-222-1211-1-2-2211-222-2-1-10-10−i3i30011−i3i3−i3i3-1i3−i3001-1-11i3−i3i3−i30000-222-20000000000001-1-11i3−i3−i3i3000000
χ592-2-22-2-222-1211-1-2-2211-222-2-1-10-10i3−i30011i3−i3i3−i3-1−i3i3001-1-11−i3i3−i3i300002-2-22000000000000-111-1i3−i3−i3i3000000
χ602-2-22-2-222-1211-1-2-2211-222-2-1-10-10i3−i30011i3−i3i3−i3-1−i3i3001-1-11−i3i3−i3i30000-222-20000000000001-1-11−i3i3i3−i3000000
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
χ6544-4-44i−4i4i−4i4-24-4-4-2224i−4i−2i−2i2i2i4i−4i0-200000-22000020000−2i−2i2i2i00000000000000000000000000000000000000
χ6644-4-44i−4i4i−4i-24-2224-4-4−2i2i4i4i−4i−4i−2i2i0-200000-22000020000−2i−2i2i2i00000000000000000000000000000000000000
χ6744-4-44i−4i4i−4i-2-2-222-222−2i2i−2i−2i2i2i−2i2i01000001-13-3-33-10000ii−i−i3i−3i−3i3i0000000000000000000000000000000000
χ6844-4-44i−4i4i−4i-2-2-222-222−2i2i−2i−2i2i2i−2i2i01000001-1-333-3-10000ii−i−i−3i3i3i−3i0000000000000000000000000000000000
χ6944-4-4−4i4i−4i4i4-24-4-4-222−4i4i2i2i−2i−2i−4i4i0-200000-220000200002i2i−2i−2i00000000000000000000000000000000000000
χ7044-4-4−4i4i−4i4i-24-2224-4-42i−2i−4i−4i4i4i2i−2i0-200000-220000200002i2i−2i−2i00000000000000000000000000000000000000
χ7144-4-4−4i4i−4i4i-2-2-222-2222i−2i2i2i−2i−2i2i−2i01000001-13-3-33-10000−i−iii−3i3i3i−3i0000000000000000000000000000000000
χ7244-4-4−4i4i−4i4i-2-2-222-2222i−2i2i2i−2i−2i2i−2i01000001-1-333-3-10000−i−iii3i−3i−3i3i0000000000000000000000000000000000
χ734-44-44i−4i−4i4i-242-22-44-4−2i2i4i−4i4i−4i2i−2i0-2000002-2000020000−2i2i−2i2i00000000000000000000000000000000000000
χ744-44-44i−4i−4i4i-2-22-222-22−2i2i−2i2i−2i2i2i−2i01000−2i32i3-11i3i3−i3−i3-10023−23i−ii−i−3−3330000000000000000000000000000000000
χ754-44-44i−4i−4i4i-2-22-222-22−2i2i−2i2i−2i2i2i−2i010002i3−2i3-11−i3−i3i3i3-100−2323i−ii−i33−3−30000000000000000000000000000000000
χ764-44-4−4i4i4i−4i-242-22-44-42i−2i−4i4i−4i4i−2i2i0-2000002-20000200002i−2i2i−2i00000000000000000000000000000000000000
χ774-44-4−4i4i4i−4i-2-22-222-222i−2i2i−2i2i−2i−2i2i01000−2i32i3-11i3i3−i3−i3-100−2323−ii−ii33−3−30000000000000000000000000000000000
χ784-44-4−4i4i4i−4i-2-22-222-222i−2i2i−2i2i−2i−2i2i010002i3−2i3-11−i3−i3i3i3-10023−23−ii−ii−3−3330000000000000000000000000000000000
χ794-4-4444-4-44-2-4-4422-244-222-2-4-40-200000220000-20000-222-200000000000000000000000000000000000000
χ804-4-4444-4-4-2-222-222-2-2-2-222-222010−2i32i300-1-1i3−i3i3−i31−2i32i3001-1-11i3−i3i3−i30000000000000000000000000000000000
χ814-4-4444-4-4-2-222-222-2-2-2-222-2220102i3−2i300-1-1−i3i3−i3i312i3−2i3001-1-11−i3i3−i3i30000000000000000000000000000000000
χ824-4-44-4-4444-2-4-4422-2-4-42-2-22440-200000220000-200002-2-2200000000000000000000000000000000000000
χ834-4-44-4-444-2-222-222-2222-2-22-2-2010−2i32i300-1-1i3−i3i3−i312i3−2i300-111-1−i3i3−i3i30000000000000000000000000000000000
χ844-4-44-4-444-2-222-222-2222-2-22-2-20102i3−2i300-1-1−i3i3−i3i31−2i32i300-111-1i3−i3i3−i30000000000000000000000000000000000

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