Finite Group Databasebeta

← Group #10590920

Character table — Group #10590920

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222222244444444444444444444444444444412121212121212121818181824242424242424243636
order12442334661212121236666688121212121212242424242424242424242424242424242244888888886612122424242444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ511111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111111-11-111-1-1-1-1
χ611111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-11-11-1-1-11111
χ711111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-1-11-1111-1-111
χ811111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111111-11-11-1-111-1-1
χ911-1-1-111111-1-1-1-11-1-1-1-111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1i−ii−iii−i−i11-1-1i−ii−ii−i
χ1011-1-1-111111-1-1-1-11-1-1-1-111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1−ii−ii−i−iii11-1-1−ii−ii−ii
χ1111-1-1-111111-1-1-1-11-1-1-1-111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111i−ii−i−i−iii-1-111i−ii−i−ii
χ1211-1-1-111111-1-1-1-11-1-1-1-111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111−ii−iiii−i−i-1-111−ii−iii−i
χ1311-1-1-111111-1-1-1-11-1-1-1-11-11-1-11111-1-1-1-1-1-1-1-1111111111-1-11i−i−iiii−i−i1-1-11i−i−ii−ii
χ1411-1-1-111111-1-1-1-11-1-1-1-11-11-1-11111-1-1-1-1-1-1-1-1111111111-1-11−iii−i−i−iii1-1-11−iii−ii−i
χ1511-1-1-111111-1-1-1-11-1-1-1-11-11-1-11111-1-1-1-1-1-1-1-111111111-111-1i−i−ii−i−iii-111-1i−i−iii−i
χ1611-1-1-111111-1-1-1-11-1-1-1-11-11-1-11111-1-1-1-1-1-1-1-111111111-111-1−iii−iii−i−i-111-1−iii−i−ii
χ17222222-122-1-1-122-12-1-1-1-122-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1222200000000-1-1-1-1000000
χ18222222-122-1-1-122-12-1-1-1-122-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2000000001111000000
χ19222222-122-1-1-122-12-1-1-1-1-2-2-1-12-1-1-1-2-2111111-2-21111112-22-200000000-11-11000000
χ20222222-122-1-1-122-12-1-1-1-1-2-2-1-12-1-1-1-2-2111111-2-2111111-22-22000000001-11-1000000
χ2122222-122-1222-1-1-1-12-1-1-122-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-10000222200000000-1-1-1-100
χ2222222-122-1222-1-1-1-12-1-1-122-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-10000-2-2-2-200000000111100
χ2322222-122-1222-1-1-1-12-1-1-1-2-2-1-1-12-1-111-2-2111111-2-21111000022-2-200000000-1-11100
χ2422222-122-1222-1-1-1-12-1-1-1-2-2-1-1-12-1-111-2-2111111-2-211110000-2-2220000000011-1-100
χ252222-222-22222222-2-2-2-220022-2-2-2-20000000000000000000000002-22-20000000000
χ262222-222-22222222-2-2-2-220022-2-2-2-2000000000000000000000000-22-220000000000
χ2722-2-2222-222-2-2-2-222222200-2-2-2-2-2-20000000000000000000000002i−2i−2i2i0000000000
χ2822-2-2222-222-2-2-2-222222200-2-2-2-2-2-2000000000000000000000000−2i2i2i−2i0000000000
χ2922-2-2-22-122-111-2-2-1-2111-12-2112-1-1-122-1-1-1-1-1-1-2-211111122-2-200000000-1-111000000
χ3022-2-2-22-122-111-2-2-1-2111-12-2112-1-1-122-1-1-1-1-1-1-2-2111111-2-2220000000011-1-1000000
χ3122-2-2-22-122-111-2-2-1-2111-1-22112-1-1-1-2-211111122-1-1-1-1-1-12-2-2200000000-111-1000000
χ3222-2-2-22-122-111-2-2-1-2111-1-22112-1-1-1-2-211111122-1-1-1-1-1-1-222-2000000001-1-11000000
χ3322-2-2-2-122-12-2-211-11-211-12-211-12-1-1-1-122-1-1-1-111-2-2111100002i−2i2i−2i00000000−ii−ii00
χ3422-2-2-2-122-12-2-211-11-211-12-211-12-1-1-1-122-1-1-1-111-2-211110000−2i2i−2i2i00000000i−ii−i00
χ3522-2-2-2-122-12-2-211-11-211-1-2211-12-1-111-2-21111-1-122-1-1-1-100002i−2i−2i2i00000000−iii−i00
χ3622-2-2-2-122-12-2-211-11-211-1-2211-12-1-111-2-21111-1-122-1-1-1-10000−2i2i2i−2i00000000i−i−ii00
χ3744444-2-24-2-2-2-2-2-21-2-21114411-2-211-2-2-2-21111-2-2-2-211110000000000000000000000
χ3844444-2-24-2-2-2-2-2-21-2-2111-4-411-2-2112222-1-1-1-12222-1-1-1-10000000000000000000000
χ394444-44-2-44-2-2-244-2-4222-200-2-2-422200000000000000000000000000000000000000
χ404444-4-24-4-2444-2-2-22-422-200-2-22-42200000000000000000000000000000000000000
χ414444-4-2-2-4-2-2-2-2-2-2122-1-11001122-1-100003i3i−3i−3i00003i3i−3i−3i0000000000000000000000
χ424444-4-2-2-4-2-2-2-2-2-2122-1-11001122-1-10000−3i−3i3i3i0000−3i−3i3i3i0000000000000000000000
χ4344-4-444-2-44-222-4-4-24-2-2-2-20022-422200000000000000000000000000000000000000
χ4444-4-44-24-4-24-4-422-2-24-2-2-200222-42200000000000000000000000000000000000000
χ4544-4-44-2-2-4-2-222221-2-211100-1-122-1-100003i3i−3i−3i0000−3i−3i3i3i0000000000000000000000
χ4644-4-44-2-2-4-2-222221-2-211100-1-122-1-10000−3i−3i3i3i00003i3i−3i−3i0000000000000000000000
χ4744-4-4-4-2-24-2-22222122-1-114-4-1-1-2-211-2-2-2-211112222-1-1-1-10000000000000000000000
χ4844-4-4-4-2-24-2-22222122-1-11-44-1-1-2-2112222-1-1-1-1-2-2-2-211110000000000000000000000
χ494-44i−4i0440-4-44i−4i4i−4i40000-4004i−4i000000000000000000000000000000000000000000
χ504-44i−4i04-20-42−2i2i4i−4i-20000200−2i2i000000i6−i6i6−i6i6−i6006−66−66−60000000000000000000000
χ514-44i−4i04-20-42−2i2i4i−4i-20000200−2i2i000000−i6i6−i6i6−i6i600−66−66−660000000000000000000000
χ524-44i−4i0-2402-44i−4i−2i2i-20000200−2i2i00006−6006−6−66i6−i600−i6i6i6−i60000000000000000000000
χ534-44i−4i0-2402-44i−4i−2i2i-20000200−2i2i0000−6600−666−6−i6i600i6−i6−i6i60000000000000000000000
χ544-44i−4i0-2-2022−2i2i−2i2i1003-3-100i−i003i−3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000000000
χ554-44i−4i0-2-2022−2i2i−2i2i1003-3-100i−i003i−3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000
χ564-44i−4i0-2-2022−2i2i−2i2i100-33-100i−i00−3i3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000
χ574-44i−4i0-2-2022−2i2i−2i2i100-33-100i−i00−3i3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000000000
χ584-4−4i4i0440-4-4−4i4i−4i4i40000-400−4i4i000000000000000000000000000000000000000000
χ594-4−4i4i04-20-422i−2i−4i4i-200002002i−2i000000i6−i6i6−i6i6−i600−66−66−660000000000000000000000
χ604-4−4i4i04-20-422i−2i−4i4i-200002002i−2i000000−i6i6−i6i6−i6i6006−66−66−60000000000000000000000
χ614-4−4i4i0-2402-4−4i4i2i−2i-200002002i−2i00006−6006−6−66−i6i600i6−i6−i6i60000000000000000000000
χ624-4−4i4i0-2402-4−4i4i2i−2i-200002002i−2i0000−6600−666−6i6−i600−i6i6i6−i60000000000000000000000
χ634-4−4i4i0-2-20222i−2i2i−2i1003-3-100−ii00−3i3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000000000
χ644-4−4i4i0-2-20222i−2i2i−2i1003-3-100−ii00−3i3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000
χ654-4−4i4i0-2-20222i−2i2i−2i100-33-100−ii003i−3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000
χ664-4−4i4i0-2-20222i−2i2i−2i100-33-100−ii003i−3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000000000

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