Finite Group Databasebeta

← Group #10590937

Character table — Group #10590937

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222222244444444444444444444444444666666661212121212121212121212121212121212121212181818183636
order1222444433666666121212121212121236668812121212242424242424242424242424242424242222444466668888121212122424242424242424224488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-111-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1
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
χ51111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1
χ91111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111i−ii−i-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-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-11111-1-1i−i−ii-1-111ii−i−i−i−iii-1-111−ii
χ111111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1-1-111−iii−i11-1-1−i−iiiii−i−i-1-111−ii
χ121111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-1−ii−ii1111−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−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111−ii−ii-1-1-1-1−i−iii−i−iii11-1-1−ii
χ141111-1-1-1-111111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-11111-1-1−iii−i-1-111−i−iiiii−i−i-1-111i−i
χ151111-1-1-1-111111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1-1-111i−i−ii11-1-1ii−i−i−i−iii-1-111i−i
χ161111-1-1-1-111111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-1i−ii−i1111ii−i−iii−i−i11-1-1−ii
χ17222222222-122-1-12-122-1-122-1-1-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10022002200-1-1002200-1-10000-1-1-1-1000000
χ18222222222-122-1-12-122-1-122-1-1-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-100-2-200-2-2001100-2-2001100001111000000
χ19222222222-122-1-12-122-1-122-1-1-1-1-1-1-2-2-1-1-1-1-2-211-2-211111111110022002200-1-100-2-200-1-100001111000000
χ20222222222-122-1-12-122-1-122-1-1-1-1-1-1-2-2-1-1-1-1-2-211-2-2111111111100-2-200-2-20011002200110000-1-1-1-1000000
χ2122222222-12-1-122-12-1-122-1-122-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122002200-1-1002200-1-100-1-1-1-10000000000
χ2222222222-12-1-122-12-1-122-1-122-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-200-2-2001100-2-200110011110000000000
χ2322222222-12-1-122-12-1-122-1-122-1-1-1-1-2-2-1-1-1-111-2-211-2-21111111122002200-1-100-2-200-1-10011110000000000
χ2422222222-12-1-122-12-1-122-1-122-1-1-1-1-2-2-1-1-1-111-2-211-2-211111111-2-200-2-200110022001100-1-1-1-10000000000
χ252222-2-2-2-22-122-1-12-1-2-211-2-211-1-1-1-12i−2i11112i2i−i−i−2i−2iii−i−i−i−iiiii002200-2-200-1-1002i−2i00110000−i−iii000000
χ262222-2-2-2-22-122-1-12-1-2-211-2-211-1-1-1-12i−2i11112i2i−i−i−2i−2iii−i−i−i−iiiii00-2-20022001100−2i2i00-1-10000ii−i−i000000
χ272222-2-2-2-22-122-1-12-1-2-211-2-211-1-1-1-1−2i2i1111−2i−2iii2i2i−i−iiiii−i−i−i−i002200-2-200-1-100−2i2i00110000ii−i−i000000
χ282222-2-2-2-22-122-1-12-1-2-211-2-211-1-1-1-1−2i2i1111−2i−2iii2i2i−i−iiiii−i−i−i−i00-2-200220011002i−2i00-1-10000−i−iii000000
χ292222-2-2-2-2-12-1-122-1211-2-211-2-2-1-1-1-12i−2i1111−i−i2i2iii−2i−2i−i−i−i−iiiii2200-2-200-1-1002i−2i001100−i−iii0000000000
χ302222-2-2-2-2-12-1-122-1211-2-211-2-2-1-1-1-12i−2i1111−i−i2i2iii−2i−2i−i−i−i−iiiii-2-20022001100−2i2i00-1-100ii−i−i0000000000
χ312222-2-2-2-2-12-1-122-1211-2-211-2-2-1-1-1-1−2i2i1111ii−2i−2i−i−i2i2iiiii−i−i−i−i2200-2-200-1-100−2i2i001100ii−i−i0000000000
χ322222-2-2-2-2-12-1-122-1211-2-211-2-2-1-1-1-1−2i2i1111ii−2i−2i−i−i2i2iiiii−i−i−i−i-2-200220011002i−2i00-1-100−i−iii0000000000
χ3322-2-22i−2i2i−2i222-22-2-2-22i−2i2i−2i2i−2i2i−2i22-2-2002i−2i2i−2i0000000000000000002-2002i−2i002-20000002i−2i00000000000000
χ3422-2-22i−2i2i−2i222-22-2-2-22i−2i2i−2i2i−2i2i−2i22-2-2002i−2i2i−2i000000000000000000-2200−2i2i00-22000000−2i2i00000000000000
χ3522-2-22i−2i2i−2i2-12-2-11-212i−2i−ii2i−2i−ii-1-11100−ii−ii00−ζ7+ζ23ζ7−ζ2300ζ5−ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13002-2002i−2i00-11000000−ii0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ3622-2-22i−2i2i−2i2-12-2-11-212i−2i−ii2i−2i−ii-1-11100−ii−ii00−ζ7+ζ23ζ7−ζ2300ζ5−ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ1300-2200−2i2i001-1000000i−i0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ3722-2-22i−2i2i−2i2-12-2-11-212i−2i−ii2i−2i−ii-1-11100−ii−ii00ζ7−ζ23−ζ7+ζ2300−ζ5+ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13002-2002i−2i00-11000000−ii0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ3822-2-22i−2i2i−2i2-12-2-11-212i−2i−ii2i−2i−ii-1-11100−ii−ii00ζ7−ζ23−ζ7+ζ2300−ζ5+ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ1300-2200−2i2i001-1000000i−i0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ3922-2-2−2i2i−2i2i222-22-2-2-2−2i2i−2i2i−2i2i−2i2i22-2-200−2i2i−2i2i0000000000000000002-200−2i2i002-2000000−2i2i00000000000000
χ4022-2-2−2i2i−2i2i222-22-2-2-2−2i2i−2i2i−2i2i−2i2i22-2-200−2i2i−2i2i000000000000000000-22002i−2i00-220000002i−2i00000000000000
χ4122-2-2−2i2i−2i2i2-12-2-11-21−2i2ii−i−2i2ii−i-1-11100i−ii−i00ζ5−ζ13−ζ5+ζ1300−ζ7+ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23002-200−2i2i00-11000000i−i0000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ4222-2-2−2i2i−2i2i2-12-2-11-21−2i2ii−i−2i2ii−i-1-11100i−ii−i00ζ5−ζ13−ζ5+ζ1300−ζ7+ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ2300-22002i−2i001-1000000−ii0000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ4322-2-2−2i2i−2i2i2-12-2-11-21−2i2ii−i−2i2ii−i-1-11100i−ii−i00−ζ5+ζ13ζ5−ζ1300ζ7−ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23002-200−2i2i00-11000000i−i0000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ4422-2-2−2i2i−2i2i2-12-2-11-21−2i2ii−i−2i2ii−i-1-11100i−ii−i00−ζ5+ζ13ζ5−ζ1300ζ7−ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ2300-22002i−2i001-1000000−ii0000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ452-22-22i−2i−2i2i22-22-22-2-2−2i2i−2i2i2i−2i2i−2i2-22-2002i−2i−2i2i00000000000000002-2002i−2i002-20000002i−2i0000000000000000
χ462-22-22i−2i−2i2i22-22-22-2-2−2i2i−2i2i2i−2i2i−2i2-22-2002i−2i−2i2i0000000000000000-2200−2i2i00-22000000−2i2i0000000000000000
χ472-22-22i−2i−2i2i-121-1-221-2i−i−2i2i−ii2i−2i-11-1100−iii−iζ5−ζ13−ζ5+ζ1300−ζ7+ζ23ζ7−ζ2300ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ232-2002i−2i00-11000000−ii00ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ482-22-22i−2i−2i2i-121-1-221-2i−i−2i2i−ii2i−2i-11-1100−iii−iζ5−ζ13−ζ5+ζ1300−ζ7+ζ23ζ7−ζ2300ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23-2200−2i2i001-1000000i−i00−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ492-22-22i−2i−2i2i-121-1-221-2i−i−2i2i−ii2i−2i-11-1100−iii−i−ζ5+ζ13ζ5−ζ1300ζ7−ζ23−ζ7+ζ2300−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ232-2002i−2i00-11000000−ii00−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ502-22-22i−2i−2i2i-121-1-221-2i−i−2i2i−ii2i−2i-11-1100−iii−i−ζ5+ζ13ζ5−ζ1300ζ7−ζ23−ζ7+ζ2300−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23-2200−2i2i001-1000000i−i00ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ512-22-2−2i2i2i−2i22-22-22-2-22i−2i2i−2i−2i2i−2i2i2-22-200−2i2i2i−2i00000000000000002-200−2i2i002-2000000−2i2i0000000000000000
χ522-22-2−2i2i2i−2i22-22-22-2-22i−2i2i−2i−2i2i−2i2i2-22-200−2i2i2i−2i0000000000000000-22002i−2i00-220000002i−2i0000000000000000
χ532-22-2−2i2i2i−2i-121-1-221-2−ii2i−2ii−i−2i2i-11-1100i−i−ii−ζ7+ζ23ζ7−ζ2300ζ5−ζ13−ζ5+ζ1300−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ132-200−2i2i00-11000000i−i00−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ542-22-2−2i2i2i−2i-121-1-221-2−ii2i−2ii−i−2i2i-11-1100i−i−ii−ζ7+ζ23ζ7−ζ2300ζ5−ζ13−ζ5+ζ1300−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13-22002i−2i001-1000000−ii00ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ552-22-2−2i2i2i−2i-121-1-221-2−ii2i−2ii−i−2i2i-11-1100i−i−iiζ7−ζ23−ζ7+ζ2300−ζ5+ζ13ζ5−ζ1300ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ132-200−2i2i00-11000000i−i00ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ562-22-2−2i2i2i−2i-121-1-221-2−ii2i−2ii−i−2i2i-11-1100i−i−iiζ7−ζ23−ζ7+ζ2300−ζ5+ζ13ζ5−ζ1300ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13-22002i−2i001-1000000−ii00−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
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χ644444-4-4-4-4-2-2-2-2-2-2-2-2222222221111−4i4i-1-1-1-12i2i2i2i−2i−2i−2i−2i−i−i−i−iiiii0000000000000000000000000000000000
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χ7044-4-4−4i4i−4i4i-2-2-22-22222i−2i2i−2i2i−2i2i−2i11-1-100−ii−ii00−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ230000000000000000000000000000000000
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χ734-44-44i−4i−4i4i-2-22-22-2222i−2i2i−2i−2i2i−2i2i1-11-100i−i−ii−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ2300ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000000000000000000000000000000
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χ814-4-44-4-4444-2-4-4224-244-2-2-4-422-222-20022-2-200000000000000000000000000000000000000000000000000
χ824-4-44-4-444-2422-4-4-24-2-24422-4-4-222-20022-2-200000000000000000000000000000000000000000000000000
χ834-4-44-4-444-2-22222-2-2-2-2-2-222221-1-1100-1-111000000003-3-333-3-330000000000000000000000000000000000
χ844-4-44-4-444-2-22222-2-2-2-2-2-222221-1-1100-1-11100000000-333-3-333-30000000000000000000000000000000000

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