Finite Group Databasebeta

← Group #13165972

Character table — Group #13165972

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222222222668888121212121212121212121212121212121212121212121212121212121616161616161616161616161616161618182424242424242424545472727272108108108108
order12443333666612121212121212122436121244666688121212121212121212121212121212121212121233336666121212121212121288242424242424242488242424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511-1-111111111-1-1-1-1-1-1-1-1-1111-1-1i−i-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1i−iiiii−i−i−i−ii−iii−i−i1-11-1
χ611-1-111111111-1-1-1-1-1-1-1-1-1111-1-1i−i-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1−iiiiii−i−i−i−i−ii−i−iii-11-11
χ711-1-111111111-1-1-1-1-1-1-1-1-1111-1-1−ii-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1i−i−i−i−i−iiiiii−iii−i−i-11-11
χ811-1-111111111-1-1-1-1-1-1-1-1-1111-1-1−ii-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−ii−i−i−i−iiiii−ii−i−iii1-11-1
χ92222222222222222222222-1-1-1-10022220022220000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1220000000022-1-1-1-10000
χ102222222222222222222222-1-1-1-10022220022220000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200000000-2-211110000
χ1122222-1-1-12-1-1-122-1-1-1-1-1-1222222222-1-1-1222-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1002-1-1-12-1-1-10000000000
χ1222222-1-1-12-1-1-122-1-1-1-1-1-1222222-2-22-1-1-1-2-22-1-1-1-2-2111111-2-21111112-1-1-12-1-1-122-1-1-1-1-1-100-2111-21110000000000
χ132222-12-1-1-12-1-1-1-122-1-1-1-122222222-12-1-122-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-100-12-1-1-12-1-10000000000
χ142222-12-1-1-12-1-1-1-122-1-1-1-1222222-2-2-12-1-1-2-2-12-1-111-2-2111111-2-21111-12-1-1-12-1-1-1-122-1-1-1-1001-2111-2110000000000
χ152222-1-12-1-1-12-1-1-1-1-122-1-122222222-1-12-122-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-12-1-1-12-1-1-1-1-122-1-100-1-12-1-1-12-10000000000
χ162222-1-12-1-1-12-1-1-1-1-122-1-1222222-2-2-1-12-1-2-2-1-12-11111-2-2111111-2-211-1-12-1-1-12-1-1-1-1-122-1-10011-2111-210000000000
χ172222-1-1-12-1-1-12-1-1-1-1-1-12222222222-1-1-1222-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-12-1-1-12-1-1-1-1-1-12200-1-1-12-1-1-120000000000
χ182222-1-1-12-1-1-12-1-1-1-1-1-122222222-2-2-1-1-12-2-2-1-1-12111111-2-2111111-2-2-1-1-12-1-1-12-1-1-1-1-1-12200111-2111-20000000000
χ1922-2-222222222-2-2-2-2-2-2-2-2-22-1-11100-2-2-2-20022220000000000000000-1-1-1-1-1-1-1-1111111112i−2i000000002i−2i−i−iii0000
χ2022-2-222222222-2-2-2-2-2-2-2-2-22-1-11100-2-2-2-20022220000000000000000-1-1-1-1-1-1-1-111111111−2i2i00000000−2i2iii−i−i0000
χ2122-2-22-1-1-12-1-1-1-2-2111111-2222-2-22i−2i-21112i−2i2-1-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii2-1-1-12-1-1-1-2-2111111002i−i−i−i−2iiii0000000000
χ2222-2-22-1-1-12-1-1-1-2-2111111-2222-2-2−2i2i-2111−2i2i2-1-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i2-1-1-12-1-1-1-2-211111100−2iiii2i−i−i−i0000000000
χ2322-2-2-12-1-1-12-1-111-2-21111-2222-2-22i−2i1-2112i−2i-12-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii-12-1-1-12-1-111-2-2111100−i2i−i−ii−2iii0000000000
χ2422-2-2-12-1-1-12-1-111-2-21111-2222-2-2−2i2i1-211−2i2i-12-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i-12-1-1-12-1-111-2-2111100i−2iii−i2i−i−i0000000000
χ2522-2-2-1-12-1-1-12-11111-2-211-2222-2-22i−2i11-212i−2i-1-12-1−i−i−i−i2i2i−i−iiiii−2i−2iii-1-12-1-1-12-11111-2-21100−i−i2i−iii−2ii0000000000
χ2622-2-2-1-12-1-1-12-11111-2-211-2222-2-2−2i2i11-21−2i2i-1-12-1iiii−2i−2iii−i−i−i−i2i2i−i−i-1-12-1-1-12-11111-2-21100ii−2ii−i−i2i−i0000000000
χ2722-2-2-1-1-12-1-1-12111111-2-2-2222-2-22i−2i111-22i−2i-1-1-12−i−i−i−i−i−i2i2iiiiiii−2i−2i-1-1-12-1-1-12111111-2-200−i−i−i2iiii−2i0000000000
χ2822-2-2-1-1-12-1-1-12111111-2-2-2222-2-2−2i2i111-2−2i2i-1-1-12iiiiii−2i−2i−i−i−i−i−i−i2i2i-1-1-12-1-1-12111111-2-200iii−2i−i−i−i2i0000000000
χ2933333333333333333333-1-1000011-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000033-1-1-1-1-1-1-1-1-1-10000-1-111
χ3033333333333333333333-1-1000011-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-3-3-1-1-1-1-1-1-1-111000011-1-1
χ3133333333333333333333-1-10000-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000003311111111-1-1000011-1-1
χ3233333333333333333333-1-10000-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-3-311111111110000-1-111
χ3333-3-333333333-3-3-3-3-3-3-3-31-10000i−i1111−ii-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i00000000000000003i−3i−i−i−i−iiiii−ii0000-111-1
χ3433-3-333333333-3-3-3-3-3-3-3-31-10000i−i1111−ii-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i0000000000000000−3i3i−i−i−i−iiiiii−i00001-1-11
χ3533-3-333333333-3-3-3-3-3-3-3-31-10000−ii1111i−i-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii00000000000000003i−3iiiii−i−i−i−i−ii00001-1-11
χ3633-3-333333333-3-3-3-3-3-3-3-31-10000−ii1111i−i-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii0000000000000000−3i3iiiii−i−i−i−ii−i0000-111-1
χ3744444-2-2-24-2-2-244-2-2-2-2-2-244-2-2-2-2004-2-2-2004-2-2-20000000000000000-2111-2111-2-211111100000000000000000000
χ384444-24-2-2-24-2-2-2-244-2-2-2-244-2-2-2-200-24-2-200-24-2-200000000000000001-2111-21111-2-2111100000000000000000000
χ394444-2-24-2-2-24-2-2-2-2-244-2-244-2-2-2-200-2-24-200-2-24-2000000000000000011-2111-211111-2-21100000000000000000000
χ404444-2-2-24-2-2-24-2-2-2-2-2-24444-2-2-2-200-2-2-2400-2-2-240000000000000000111-2111-2111111-2-200000000000000000000
χ4144-4-44-2-2-24-2-2-2-4-4222222-44-2-22200-4222004-2-2-20000000000000000-2111-211122-1-1-1-1-1-100000000000000000000
χ4244-4-4-24-2-2-24-2-222-4-42222-44-2-222002-42200-24-2-200000000000000001-2111-211-1-122-1-1-1-100000000000000000000
χ4344-4-4-2-24-2-2-24-22222-4-422-44-2-2220022-4200-2-24-2000000000000000011-2111-21-1-1-1-122-1-100000000000000000000
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χ454-44i−4i4444-4-4-4-44i−4i4i−4i4i−4i4i−4i001-1i−i00000000000000000000000000001111-1-1-1-1i−ii−ii−ii−i000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
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χ474-44i−4i4444-4-4-4-44i−4i4i−4i4i−4i4i−4i00-22−2i2i0000000000000000000000000000-2-2-2-22222−2i2i−2i2i−2i2i−2i2i00000000000000000000
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χ6866666-3-3-36-3-3-366-3-3-3-3-3-3-2-20000-2-2-211122-2111-2-2111111-2-21111110000000000000000002-1-1-12-1-1-10000000000
χ696666-36-3-3-36-3-3-3-366-3-3-3-3-2-20000221-211-2-21-211-1-122-1-1-1-1-1-122-1-1-1-10000000000000000001-2111-2110000000000
χ706666-36-3-3-36-3-3-3-366-3-3-3-3-2-20000-2-21-211221-21111-2-2111111-2-21111000000000000000000-12-1-1-12-1-10000000000
χ716666-3-36-3-3-36-3-3-3-3-366-3-3-2-200002211-21-2-211-21-1-1-1-122-1-1-1-1-1-122-1-100000000000000000011-2111-210000000000
χ726666-3-36-3-3-36-3-3-3-3-366-3-3-2-20000-2-211-212211-211111-2-2111111-2-211000000000000000000-1-12-1-1-12-10000000000
χ736666-3-3-36-3-3-36-3-3-3-3-3-366-2-2000022111-2-2-2111-2-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000111-2111-20000000000
χ746666-3-3-36-3-3-36-3-3-3-3-3-366-2-20000-2-2111-222111-2111111-2-2111111-2-2000000000000000000-1-1-12-1-1-120000000000
χ7566-6-66-3-3-36-3-3-3-6-63333332-200002i−2i2-1-1-1−2i2i-21112i2i−i−i−i−i−i−i−2i−2iiiiiii000000000000000000−2iiii2i−i−i−i0000000000
χ7666-6-66-3-3-36-3-3-3-6-63333332-20000−2i2i2-1-1-12i−2i-2111−2i−2iiiiiii2i2i−i−i−i−i−i−i0000000000000000002i−i−i−i−2iiii0000000000
χ7766-6-6-36-3-3-36-3-333-6-633332-200002i−2i-12-1-1−2i2i1-211−i−i2i2i−i−i−i−iii−2i−2iiiii000000000000000000i−2iii−i2i−i−i0000000000
χ7866-6-6-36-3-3-36-3-333-6-633332-20000−2i2i-12-1-12i−2i1-211ii−2i−2iiiii−i−i2i2i−i−i−i−i000000000000000000−i2i−i−ii−2iii0000000000
χ7966-6-6-3-36-3-3-36-33333-6-6332-200002i−2i-1-12-1−2i2i11-21−i−i−i−i2i2i−i−iiiii−2i−2iii000000000000000000ii−2ii−i−i2i−i0000000000
χ8066-6-6-3-36-3-3-36-33333-6-6332-20000−2i2i-1-12-12i−2i11-21iiii−2i−2iii−i−i−i−i2i2i−i−i000000000000000000−i−i2i−iii−2ii0000000000
χ8166-6-6-3-3-36-3-3-36333333-6-62-200002i−2i-1-1-12−2i2i111-2−i−i−i−i−i−i2i2iiiiiii−2i−2i000000000000000000iii−2i−i−i−i2i0000000000
χ8266-6-6-3-3-36-3-3-36333333-6-62-20000−2i2i-1-1-122i−2i111-2iiiiii−2i−2i−i−i−i−i−i−i2i2i000000000000000000−i−i−i2iiii−2i0000000000
χ838-88i−8i8-4-4-4-84448i−8i−4i4i−4i4i−4i4i002-22i−2i00000000000000000000000000002-1-1-1-21112i−2i−ii−ii−ii00000000000000000000
χ848-88i−8i-48-4-44-844−4i4i8i−8i−4i4i−4i4i002-22i−2i0000000000000000000000000000-12-1-11-211−ii2i−2i−ii−ii00000000000000000000
χ858-88i−8i-4-48-444-84−4i4i−4i4i8i−8i−4i4i002-22i−2i0000000000000000000000000000-1-12-111-21−ii−ii2i−2i−ii00000000000000000000
χ868-88i−8i-4-4-48444-8−4i4i−4i4i−4i4i8i−8i002-22i−2i0000000000000000000000000000-1-1-12111-2−ii−ii−ii2i−2i00000000000000000000
χ878-8−8i8i8-4-4-4-8444−8i8i4i−4i4i−4i4i−4i002-2−2i2i00000000000000000000000000002-1-1-1-2111−2i2ii−ii−ii−i00000000000000000000
χ888-8−8i8i-48-4-44-8444i−4i−8i8i4i−4i4i−4i002-2−2i2i0000000000000000000000000000-12-1-11-211i−i−2i2ii−ii−i00000000000000000000
χ898-8−8i8i-4-48-444-844i−4i4i−4i−8i8i4i−4i002-2−2i2i0000000000000000000000000000-1-12-111-21i−ii−i−2i2ii−i00000000000000000000
χ908-8−8i8i-4-4-48444-84i−4i4i−4i4i−4i−8i8i002-2−2i2i0000000000000000000000000000-1-1-12111-2i−ii−ii−i−2i2i00000000000000000000

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