Finite Group Databasebeta

← Group #10590735

Character table — Group #10590735

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222222244444444444444444444444444666666661212121212121212121212121212121212121212181818183636
order1222444433666666121212121212121236668812121212242424242424242424242424242424248888888822446666121212122424242424242424444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11-11-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-11111-11-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-1
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
χ51111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ61111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-111-1-1111111-1-1-1-1-1-1-1-111
χ71111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-111-1-111-1-1-1-1-1-11111-1-1-1-111
χ81111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1
χ91111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−iii−i−i11-1-11111-1-1-1-1ii−i−iii−i−i11-1-1i−i
χ101111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i−i−iii1-1-1111-1-1-1-111ii−i−i−i−iii-1-111−ii
χ111111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i−i−iiiii−i−i-111-1-1-11111-1-1−i−iiiii−i−i-1-111−ii
χ121111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i−i−iii−i−iii-1-111-1-1-1-11111−i−iii−i−iii11-1-1i−i
χ131111-1-1-1-111111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−iii−i−iii−i−i−i−iiiiiii−i−iii−i−i-1-111-1-1-1-11111ii−i−iii−i−i11-1-1−ii
χ141111-1-1-1-111111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−iii−i−iii−i−i−i−iiiiiii−i−i−i−iii-111-1-1-11111-1-1ii−i−i−i−iii-1-111i−i
χ151111-1-1-1-111111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iiiii−i−i1-1-1111-1-1-1-111−i−iiiii−i−i-1-111i−i
χ161111-1-1-1-111111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii−i−iii11-1-11111-1-1-1-1−i−iii−i−iii11-1-1−ii
χ17222222222-122-1-12-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222200002020-1-100-1-100-1-1-1-10000000000
χ18222222222-122-1-12-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-20000-20-201100110011110000000000
χ19222222222-122-1-12-122-1-1-1-122-1-1-1-1-2-2-1-1-1-11111-2-2-2-21111111122220000-20-2011001100-1-1-1-10000000000
χ20222222222-122-1-12-122-1-1-1-122-1-1-1-1-2-2-1-1-1-11111-2-2-2-211111111-2-2-2-200002020-1-100-1-10011110000000000
χ2122222222-12-1-122-12-1-12222-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100002222020200-1-100-1-10000-1-1-1-1000000
χ2222222222-12-1-122-12-1-12222-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-20-20-20011001100001111000000
χ2322222222-12-1-122-12-1-12222-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2-2111111111111000022220-20-2001100110000-1-1-1-1000000
χ2422222222-12-1-122-12-1-12222-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2-21111111111110000-2-2-2-2020200-1-100-1-100001111000000
χ252222-2-2-2-22-122-1-12-1-2-21111-2-2-1-1-1-12i−2i1111−i−iii2i2i−2i−2i−i−i−i−iiiii2i2i−2i−2i000020-20-1-1001100−i−iii0000000000
χ262222-2-2-2-22-122-1-12-1-2-21111-2-2-1-1-1-12i−2i1111−i−iii2i2i−2i−2i−i−i−i−iiiii−2i−2i2i2i0000-20201100-1-100ii−i−i0000000000
χ272222-2-2-2-22-122-1-12-1-2-21111-2-2-1-1-1-1−2i2i1111ii−i−i−2i−2i2i2iiiii−i−i−i−i2i2i−2i−2i0000-20201100-1-100−i−iii0000000000
χ282222-2-2-2-22-122-1-12-1-2-21111-2-2-1-1-1-1−2i2i1111ii−i−i−2i−2i2i2iiiii−i−i−i−i−2i−2i2i2i000020-20-1-1001100ii−i−i0000000000
χ292222-2-2-2-2-12-1-122-1211-2-2-2-211-1-1-1-12i−2i11112i2i−2i−2i−i−iii−i−i−i−iiiii00002i2i−2i−2i020-200-1-100110000−i−iii000000
χ302222-2-2-2-2-12-1-122-1211-2-2-2-211-1-1-1-12i−2i11112i2i−2i−2i−i−iii−i−i−i−iiiii0000−2i−2i2i2i0-202001100-1-10000ii−i−i000000
χ312222-2-2-2-2-12-1-122-1211-2-2-2-211-1-1-1-1−2i2i1111−2i−2i2i2iii−i−iiiii−i−i−i−i00002i2i−2i−2i0-202001100-1-10000−i−iii000000
χ322222-2-2-2-2-12-1-122-1211-2-2-2-211-1-1-1-1−2i2i1111−2i−2i2i2iii−i−iiiii−i−i−i−i0000−2i−2i2i2i020-200-1-100110000ii−i−i000000
χ3322-2-222-2-222-2-2-2-22222-2-222-2-22-2-220022-2-2000000000000000000002i−2i2i−2i00000000000000002i−2i2i−2i000000
χ3422-2-222-2-222-2-2-2-22222-2-222-2-22-2-220022-2-200000000000000000000−2i2i−2i2i0000000000000000−2i2i−2i2i000000
χ3522-2-222-2-2-1211-2-2-12-1-1-2-22211-111-100-1-11100003−33−333−3−333−3−300002i−2i2i−2i000000−i3i300−i3i30000−ii−ii000000
χ3622-2-222-2-2-1211-2-2-12-1-1-2-22211-111-100-1-11100003−33−333−3−333−3−30000−2i2i−2i2i000000i3−i300i3−i30000i−ii−i000000
χ3722-2-222-2-2-1211-2-2-12-1-1-2-22211-111-100-1-1110000−33−33−3−333−3−33300002i−2i2i−2i000000i3−i300i3−i30000−ii−ii000000
χ3822-2-222-2-2-1211-2-2-12-1-1-2-22211-111-100-1-1110000−33−33−3−333−3−3330000−2i2i−2i2i000000−i3i300−i3i30000i−ii−i000000
χ3922-2-2-2-22222-2-2-2-222-2-222-2-2222-2-2200-2-222000000000000000000002-2-2200000000000000002-2-22000000
χ4022-2-2-2-22222-2-2-2-222-2-222-2-2222-2-2200-2-22200000000000000000000-222-20000000000000000-222-2000000
χ4122-2-2-2-222-1211-2-2-121122-2-2-1-1-111-10011-1-10000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i300002-2-22000000−i3i300i3−i30000-111-1000000
χ4222-2-2-2-222-1211-2-2-121122-2-2-1-1-111-10011-1-10000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i30000-222-2000000i3−i300−i3i300001-1-11000000
χ4322-2-2-2-222-1211-2-2-121122-2-2-1-1-111-10011-1-10000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i300002-2-22000000i3−i300−i3i30000-111-1000000
χ4422-2-2-2-222-1211-2-2-121122-2-2-1-1-111-10011-1-10000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i30000-222-2000000−i3i300i3−i300001-1-11000000
χ452-22-22i−2i2i−2i222-22-2-2-22i−2i2i−2i2i−2i2i−2i22-2-2002i−2i2i−2i000000000000000000000000000000000000000000002-22i−2i00
χ462-22-22i−2i2i−2i222-22-2-2-22i−2i2i−2i2i−2i2i−2i22-2-2002i−2i2i−2i00000000000000000000000000000000000000000000-22−2i2i00
χ472-22-2−2i2i−2i2i222-22-2-2-2−2i2i−2i2i−2i2i−2i2i22-2-200−2i2i−2i2i000000000000000000000000000000000000000000002-2−2i2i00
χ482-22-2−2i2i−2i2i222-22-2-2-2−2i2i−2i2i−2i2i−2i2i22-2-200−2i2i−2i2i00000000000000000000000000000000000000000000-222i−2i00
χ492-2-222i−2i−2i2i22-22-22-2-22i−2i−2i2i2i−2i−2i2i2-22-2002i−2i−2i2i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000
χ502-2-222i−2i−2i2i22-22-22-2-22i−2i−2i2i2i−2i−2i2i2-22-2002i−2i−2i2i00000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000
χ512-2-222i−2i−2i2i2-1-221-1-212i−2ii−i−ii−2i2i-11-1100−iii−iζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000−i3i3003−300ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ230000000000
χ522-2-222i−2i−2i2i2-1-221-1-212i−2ii−i−ii−2i2i-11-1100−iii−iζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000i3−i300−3300−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ230000000000
χ532-2-222i−2i−2i2i2-1-221-1-212i−2ii−i−ii−2i2i-11-1100−iii−i−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000i3−i300−3300ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ230000000000
χ542-2-222i−2i−2i2i2-1-221-1-212i−2ii−i−ii−2i2i-11-1100−iii−i−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000−i3i3003−300−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ230000000000
χ552-2-22−2i2i2i−2i22-22-22-2-2−2i2i2i−2i−2i2i2i−2i2-22-200−2i2i2i−2i00000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000
χ562-2-22−2i2i2i−2i22-22-22-2-2−2i2i2i−2i−2i2i2i−2i2-22-200−2i2i2i−2i0000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000
χ572-2-22−2i2i2i−2i2-1-221-1-21−2i2i−iii−i2i−2i-11-1100i−i−ii−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000i3−i3003−300−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000000000
χ582-2-22−2i2i2i−2i2-1-221-1-21−2i2i−iii−i2i−2i-11-1100i−i−ii−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000−i3i300−3300ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000000000
χ592-2-22−2i2i2i−2i2-1-221-1-21−2i2i−iii−i2i−2i-11-1100i−i−iiζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000−i3i300−3300−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000000000
χ602-2-22−2i2i2i−2i2-1-221-1-21−2i2i−iii−i2i−2i-11-1100i−i−iiζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000i3−i3003−300ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000000000
χ6144444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111441111-2-2-2-2-2-2-2-2111111110000000000000000000000000000000000
χ6244444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111-4-4111122222222-1-1-1-1-1-1-1-10000000000000000000000000000000000
χ634444-4-4-4-4-2-2-2-2-2-2-2-22222222211114i−4i-1-1-1-1−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i0000000000000000000000000000000000
χ644444-4-4-4-4-2-2-2-2-2-2-2-2222222221111−4i4i-1-1-1-12i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii0000000000000000000000000000000000
χ6544-4-444-4-44-2-4-4224-24422-2-2-4-4-222-200-2-22200000000000000000000000000000000000000000000000000
χ6644-4-444-4-4-2-22222-2-2-2-222-2-2221-1-110011-1-1000023−2323−23−3−333−3−3330000000000000000000000000000000000
χ6744-4-444-4-4-2-22222-2-2-2-222-2-2221-1-110011-1-10000−2323−232333−3−333−3−30000000000000000000000000000000000
χ6844-4-4-4-4444-2-4-4224-2-4-4-2-22244-222-20022-2-200000000000000000000000000000000000000000000000000
χ6944-4-4-4-444-2-22222-2-222-2-222-2-21-1-1100-1-1110000−2i32i32i3−2i3i3i3−i3−i3−i3−i3i3i30000000000000000000000000000000000
χ7044-4-4-4-444-2-22222-2-222-2-222-2-21-1-1100-1-11100002i3−2i3−2i32i3−i3−i3i3i3i3i3−i3−i30000000000000000000000000000000000
χ714-44-44i−4i4i−4i4-24-4-22-424i−4i−2i2i−2i2i4i−4i-2-22200−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ724-44-44i−4i4i−4i-24-224-42-4−2i2i4i−4i4i−4i−2i2i-2-22200−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ734-44-44i−4i4i−4i-2-2-22-2222−2i2i−2i2i−2i2i−2i2i11-1-100i−ii−i000000003ζ7+3ζ23−3ζ7−3ζ23−3ζ7−3ζ233ζ7+3ζ23−3ζ5−3ζ133ζ5+3ζ133ζ5+3ζ13−3ζ5−3ζ130000000000000000000000000000000000
χ744-44-44i−4i4i−4i-2-2-22-2222−2i2i−2i2i−2i2i−2i2i11-1-100i−ii−i00000000−3ζ7−3ζ233ζ7+3ζ233ζ7+3ζ23−3ζ7−3ζ233ζ5+3ζ13−3ζ5−3ζ13−3ζ5−3ζ133ζ5+3ζ130000000000000000000000000000000000
χ754-44-4−4i4i−4i4i4-24-4-22-42−4i4i2i−2i2i−2i−4i4i-2-222002i−2i2i−2i00000000000000000000000000000000000000000000000000
χ764-44-4−4i4i−4i4i-24-224-42-42i−2i−4i4i−4i4i2i−2i-2-222002i−2i2i−2i00000000000000000000000000000000000000000000000000
χ774-44-4−4i4i−4i4i-2-2-22-22222i−2i2i−2i2i−2i2i−2i11-1-100−ii−ii00000000−3ζ5−3ζ133ζ5+3ζ133ζ5+3ζ13−3ζ5−3ζ133ζ7+3ζ23−3ζ7−3ζ23−3ζ7−3ζ233ζ7+3ζ230000000000000000000000000000000000
χ784-44-4−4i4i−4i4i-2-2-22-22222i−2i2i−2i2i−2i2i−2i11-1-100−ii−ii000000003ζ5+3ζ13−3ζ5−3ζ13−3ζ5−3ζ133ζ5+3ζ13−3ζ7−3ζ233ζ7+3ζ233ζ7+3ζ23−3ζ7−3ζ230000000000000000000000000000000000
χ794-4-444i−4i−4i4i-242-2-442-4−2i2i−4i4i4i−4i2i−2i-22-2200−2i2i2i−2i00000000000000000000000000000000000000000000000000
χ804-4-444i−4i−4i4i-2-22-22-222−2i2i2i−2i−2i2i2i−2i1-11-100i−i−ii2ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ230000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000000000000000000000000000
χ814-4-444i−4i−4i4i-2-22-22-222−2i2i2i−2i−2i2i2i−2i1-11-100i−i−ii−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ230000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000000000000000000000000000000
χ824-4-44−4i4i4i−4i-242-2-442-42i−2i4i−4i−4i4i−2i2i-22-22002i−2i−2i2i00000000000000000000000000000000000000000000000000
χ834-4-44−4i4i4i−4i-2-22-22-2222i−2i−2i2i2i−2i−2i2i1-11-100−iii−i−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ130000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000000000000000000000000
χ844-4-44−4i4i4i−4i-2-22-22-2222i−2i−2i2i2i−2i−2i2i1-11-100−iii−i2ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ130000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000000000000000000000000000

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