Finite Group Databasebeta

← Group #13165164

Character table — Group #13165164

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122224444444466888888881212121212121212121212121818242424242424242424242424242424243636363636363636363636363636363654547272108108
order12443612123366121212122433661212121224666688121212122466661212121224242424242424242444666881212121212121224242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-111-1-1111-1-1111-1-1-1-111-1-1-1-1
χ311111111111111111111111111-1-111-1-11111-1-111-11-1-1-11-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ411111111111111111111111111-1-111-1-1-1-111-1-111-11-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-11-1-1111111-1-111
χ51111111111111111-1-11111111111-1-11111-1-111111-1111-11111111111-1-111-1-11-1-11-1-11111-1-1-1-1-1-1
χ61111111111111111-1-11111111111-1-111-1-1-1-111111-1111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1111-1-1111-1-1-1-1-1-1-1-111
χ81111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1
χ911-1-111-1-11111-1-1-1-11-11111-1-1-1-11-11111i−i-1-1-1-1-111111-1-1-1-1i−ii−iii−i−i1-1i−i11-1i−i1-1-1ii−i−i-11i−ii−i
χ1011-1-111-1-11111-1-1-1-11-11111-1-1-1-11-11111−ii-1-1-1-1-111111-1-1-1-1−ii−ii−i−iii1-1−ii11-1−ii1-1-1−i−iii-11−ii−ii
χ1111-1-111-1-11111-1-1-1-11-11111-1-1-1-1-1111-1-1i−i-1-111-11-11-1-11-111i−ii−iii−i−i-11−ii-1-1-1i−i111−i−iii-11i−i−ii
χ1211-1-111-1-11111-1-1-1-11-11111-1-1-1-1-1111-1-1−ii-1-111-11-11-1-11-111−ii−ii−i−iii-11i−i-1-1-1−ii111ii−i−i-11−iii−i
χ1311-1-111-1-11111-1-1-1-1-111111-1-1-1-11-1-1-111i−i11-1-1-111-111-11-1-1i−ii−iii−i−i-11i−i-1-1-1−ii111ii−i−i1-1−ii−ii
χ1411-1-111-1-11111-1-1-1-1-111111-1-1-1-11-1-1-111−ii11-1-1-111-111-11-1-1−ii−ii−i−iii-11−ii-1-1-1i−i111−i−iii1-1i−ii−i
χ1511-1-111-1-11111-1-1-1-1-111111-1-1-1-1-11-1-1-1-1i−i1111-11-1-1-1-11111i−ii−iii−i−i1-1−ii11-1−ii1-1-1−i−iii1-1−iii−i
χ1611-1-111-1-11111-1-1-1-1-111111-1-1-1-1-11-1-1-1-1−ii1111-11-1-1-1-11111−ii−ii−i−iii1-1i−i11-1i−i1-1-1ii−i−i1-1i−i−ii
χ1722222222222222222222222222002200002200-2-20200020000000000000000-200-2000000-2-20000
χ182222222222222222-2-22222222200-2-20000-2-200-2-20-2000-20000000000000000-200-2000000220000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-122002222002222-10-1-1-10-1-1-1-122-1-1-1-1002200-100-100-1-1-1-1000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-1220022-2-2002222-10-1-1-10-1-111-2-2111100-2-200-100-1001111000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-200-2-22200-2-22210111011-1-122-1-1-1-100-2-200-100-1001111000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-200-2-2-2-200-2-2221011101111-2-21111002200-100-100-1-1-1-1000000
χ2322-2-222-2-22222-2-2-2-22-22222-2-2-2-200220000-2-2002-202000-20000000000000000200-20000002-20000
χ2422-2-222-2-22222-2-2-2-2-222222-2-2-2-200-2-2000022002-20-200020000000000000000200-2000000-220000
χ2522-2-2-1-1112222-2-2-2-200-1-1-1-111112-200222i−2i00-2-2-22-10-1-11011−ii2i−2i−i−iii002i−2i00100-100−i−iii000000
χ2622-2-2-1-1112222-2-2-2-200-1-1-1-111112-20022−2i2i00-2-2-22-10-1-11011i−i−2i2iii−i−i00−2i2i00100-100ii−i−i000000
χ2722-2-2-1-1112222-2-2-2-200-1-1-1-11111-2200-2-22i−2i0022-221011-10-1-1−ii2i−2i−i−iii00−2i2i00100-100ii−i−i000000
χ2822-2-2-1-1112222-2-2-2-200-1-1-1-11111-2200-2-2−2i2i0022-221011-10-1-1i−i−2i2iii−i−i002i−2i00100-100−i−iii000000
χ29444444441-21-2-2-211441-21-2-2-21100-2-20022-2-200000100010022-1-1-1-1-1-1000000022000000000-1-100
χ30444444441-21-2-2-211441-21-2-2-21100-2-200-2-2-2-2000001000100-2-21111110000000-2-20000000001100
χ31444444441-21-2-2-211-4-41-21-2-2-211002200222200000-1000-10022-1-1-1-1-1-10000000-2-20000000001100
χ32444444441-21-2-2-211-4-41-21-2-2-211002200-2-22200000-1000-100-2-2111111000000022000000000-1-100
χ3344444444-21-2111-2-244-21-2111-2-22211-1-10011-1-1002-2-1-12-2-1-1000000002200-1-10000-1-10000000000
χ3444444444-21-2111-2-244-21-2111-2-2-2-2111100111100-2-211-2-21100000000-2-200110000110000000000
χ3544444444-21-2111-2-2-4-4-21-2111-2-222-1-1-1-100-1-1-1-10022-1-122-1-100000000-2-200110000110000000000
χ3644444444-21-2111-2-2-4-4-21-2111-2-2-2-2-1-11100-1-11100-2211-2211000000002200-1-10000-1-10000000000
χ374444-2-2-2-24444444400-2-2-2-2-2-2-2-2000000000000-4-400000000000000000000002002000000000000
χ3844-4-444-4-41-21-222-1-14-41-21-222-1-100-2-2002i−2i22000001000-1002i−2i−ii−i−iii00000002i−2i000000000−ii00
χ3944-4-444-4-41-21-222-1-14-41-21-222-1-100-2-200−2i2i22000001000-100−2i2ii−iii−i−i0000000−2i2i000000000i−i00
χ4044-4-444-4-41-21-222-1-1-441-21-222-1-10022002i−2i-2-200000-10001002i−2i−ii−i−iii0000000−2i2i000000000i−i00
χ4144-4-444-4-41-21-222-1-1-441-21-222-1-1002200−2i2i-2-200000-1000100−2i2ii−iii−i−i00000002i−2i000000000−ii00
χ4244-4-444-4-4-21-21-1-1224-4-21-21-1-1222-211-1-100-1-111002-2-1-1-2211000000002-200-1-10000110000000000
χ4344-4-444-4-4-21-21-1-1224-4-21-21-1-122-22111100-1-1-1-100-2-21122-1-100000000-2200110000-1-10000000000
χ4444-4-444-4-4-21-21-1-122-44-21-21-1-1222-2-1-1-1-10011110022-1-1-2-21100000000-2200110000-1-10000000000
χ4544-4-444-4-4-21-21-1-122-44-21-21-1-122-22-1-1110011-1-100-22112-2-1-1000000002-200-1-10000110000000000
χ4644-4-4-2-2224444-4-4-4-400-2-2-2-222220000000000004-40000000000000000000000-2002000000000000
χ474-44i−4i4-44i−4i44-4-44i−4i4i−4i0044-4-44i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ484-44i−4i4-44i−4i-212-1i−i−2i2i00-212-1i−i−2i2i003-3−i3i3003i−3i3−30000−i3i3003−3000000000000−i3i300003−30000000000
χ494-44i−4i4-44i−4i-212-1i−i−2i2i00-212-1i−i−2i2i003-3i3−i3003i−3i−330000i3−i300−33000000000000i3−i30000−330000000000
χ504-44i−4i4-44i−4i-212-1i−i−2i2i00-212-1i−i−2i2i00-33−i3i300−3i3i3−30000−i3i3003−3000000000000i3−i30000−330000000000
χ514-44i−4i4-44i−4i-212-1i−i−2i2i00-212-1i−i−2i2i00-33i3−i300−3i3i−330000i3−i300−33000000000000−i3i300003−30000000000
χ524-44i−4i-22−2i2i44-4-44i−4i4i−4i00-2-222−2i2i−2i2i000000000000000000000000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000
χ534-44i−4i-22−2i2i44-4-44i−4i4i−4i00-2-222−2i2i−2i2i000000000000000000000000000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000
χ544-4−4i4i4-4−4i4i44-4-4−4i4i−4i4i0044-4-4−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ554-4−4i4i4-4−4i4i-212-1−ii2i−2i00-212-1−ii2i−2i003-3−i3i300−3i3i−330000−i3i300−33000000000000−i3i30000−330000000000
χ564-4−4i4i4-4−4i4i-212-1−ii2i−2i00-212-1−ii2i−2i003-3i3−i300−3i3i3−30000i3−i3003−3000000000000i3−i300003−30000000000
χ574-4−4i4i4-4−4i4i-212-1−ii2i−2i00-212-1−ii2i−2i00-33−i3i3003i−3i−330000−i3i300−33000000000000i3−i300003−30000000000
χ584-4−4i4i4-4−4i4i-212-1−ii2i−2i00-212-1−ii2i−2i00-33i3−i3003i−3i3−30000i3−i3003−3000000000000−i3i30000−330000000000
χ594-4−4i4i-222i−2i44-4-4−4i4i−4i4i00-2-2222i−2i2i−2i000000000000000000000000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000
χ604-4−4i4i-222i−2i44-4-4−4i4i−4i4i00-2-2222i−2i2i−2i000000000000000000000000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000
χ618888-4-4-4-42-42-4-4-42200-12-1222-1-10000004400000000000000-2-2-2-211110000000000000000000000
χ628888-4-4-4-42-42-4-4-42200-12-1222-1-1000000-4-4000000000000002222-1-1-1-10000000000000000000000
χ638888-4-4-4-4-42-4222-4-4002-12-1-1-1224400-2-20000-2-200-2011-2011000000000000000000000000000000
χ648888-4-4-4-4-42-4222-4-4002-12-1-1-122-4-400220000220020-1-120-1-1000000000000000000000000000000
χ6588-8-8-4-4442-42-444-2-200-12-12-2-2110000004i−4i00000000000000−2i2i−2i2iii−i−i0000000000000000000000
χ6688-8-8-4-4442-42-444-2-200-12-12-2-211000000−4i4i000000000000002i−2i2i−2i−i−iii0000000000000000000000
χ6788-8-8-4-444-42-42-2-244002-12-111-2-24-400-2-200002200-201120-1-1000000000000000000000000000000
χ6888-8-8-4-444-42-42-2-244002-12-111-2-2-4400220000-2-20020-1-1-2011000000000000000000000000000000
χ698-88i−8i8-88i−8i2-4-24−4i4i2i−2i002-4-24−4i4i2i−2i0000000000000000000000000000000000000000000000000000
χ708-88i−8i-44−4i4i2-4-24−4i4i2i−2i00-121-22i−2i−ii000000000000000000000000003ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ130000000000000000000000
χ718-88i−8i-44−4i4i2-4-24−4i4i2i−2i00-121-22i−2i−ii00000000000000000000000000−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ130000000000000000000000
χ728-88i−8i-44−4i4i-424-22i−2i−4i4i002-1-21−ii2i−2i0000−2i32i3000023−230000i3−i300−33000000000000000000000000000000
χ738-88i−8i-44−4i4i-424-22i−2i−4i4i002-1-21−ii2i−2i00002i3−2i30000−23230000−i3i3003−3000000000000000000000000000000
χ748-8−8i8i8-8−8i8i2-4-244i−4i−2i2i002-4-244i−4i−2i2i0000000000000000000000000000000000000000000000000000
χ758-8−8i8i-444i−4i2-4-244i−4i−2i2i00-121-2−2i2ii−i00000000000000000000000000−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ230000000000000000000000
χ768-8−8i8i-444i−4i2-4-244i−4i−2i2i00-121-2−2i2ii−i000000000000000000000000003ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ230000000000000000000000
χ778-8−8i8i-444i−4i-424-2−2i2i4i−4i002-1-21i−i−2i2i0000−2i32i30000−23230000i3−i3003−3000000000000000000000000000000
χ788-8−8i8i-444i−4i-424-2−2i2i4i−4i002-1-21i−i−2i2i00002i3−2i3000023−230000−i3i300−33000000000000000000000000000000

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