Finite Group Databasebeta

← Group #11771252

Character table — Group #11771252

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122224444444444444444488888888181824242424242424242424242424242424242424242424242436363672727272
order1222444423366666612121212121212126666121212122288888888242424242424242424242424242424242444444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ5111111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1ii−i−i
χ6111111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1−i−iii
χ7111111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i11-1−i−iii
χ8111111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii11-1ii−i−i
χ91111-1-111-111111111-1-1-1-11111-1-1-1-1-1-111-1-1i−ii−i1-11-1ii−i−iii−i−i11-1-111-1-11-11i−ii−i
χ101111-1-111-111111111-1-1-1-11111-1-1-1-1-1-111-1-1i−ii−i-11-11ii−i−iii−i−i-1-111-1-1111-11−ii−ii
χ111111-1-111-111111111-1-1-1-11111-1-1-1-1-1-111-1-1−ii−ii1-11-1−i−iii−i−iii11-1-111-1-11-11−ii−ii
χ121111-1-111-111111111-1-1-1-11111-1-1-1-1-1-111-1-1−ii−ii-11-11−i−iii−i−iii-1-111-1-1111-11i−ii−i
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii1-1-1-111-1
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i1-1-11-1-11
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii1-1-11-1-11
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i1-1-1-111-1
χ17222222222222222222222222222222222-2-2000000000000000000000000-2-2-20000
χ18222222-2-2-2222222222222-2-2-2-2-2-2-2-222-2-222000000000000000000000000-2-220000
χ192222-2-222-222222222-2-2-2-22222-2-2-2-2-2-22222000000000000000000000000-22-20000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000000000000-2220000
χ214444444441-211-2-21-21111-2-2-2-211-2-2-2-2110022220000-1-1-1-1-1-1-1-1000000000000000
χ224444444441-211-2-21-21111-2-2-2-211-2-2-2-21100-2-2-2-2000011111111000000000000000
χ23444444444-21-2-211-21-2-2-2-21111-2-21111-2-2000000222200000000-1-1-1-1-1-1-1-10000000
χ24444444444-21-2-211-21-2-2-2-21111-2-21111-2-2000000-2-2-2-200000000111111110000000
χ25444444-4-4-41-211-2-21-211112222-1-122-2-2-1-10022-2-20000-1-1-1-11111000000000000000
χ26444444-4-4-41-211-2-21-211112222-1-122-2-2-1-100-2-22200001111-1-1-1-1000000000000000
χ27444444-4-4-4-21-2-211-21-2-2-2-2-1-1-1-122-1-111220000002i2i−2i−2i00000000−i−i−i−iiiii0000000
χ28444444-4-4-4-21-2-211-21-2-2-2-2-1-1-1-122-1-11122000000−2i−2i2i2i00000000iiii−i−i−i−i0000000
χ294444-4-444-41-211-2-21-2-1-1-1-1-2-2-2-2-1-1222211002i−2i2i−2i0000−i−iii−i−iii000000000000000
χ304444-4-444-41-211-2-21-2-1-1-1-1-2-2-2-2-1-122221100−2i2i−2i2i0000ii−i−iii−i−i000000000000000
χ314444-4-444-4-21-2-211-212222111122-1-1-1-1-2-20000002-22-200000000-1-111-1-1110000000
χ324444-4-444-4-21-2-211-212222111122-1-1-1-1-2-2000000-22-220000000011-1-111-1-10000000
χ334444-4-4-4-441-211-2-21-2-1-1-1-1222211-2-222-1-1002i−2i−2i2i0000−i−iiiii−i−i000000000000000
χ344444-4-4-4-441-211-2-21-2-1-1-1-1222211-2-222-1-100−2i2i2i−2i0000ii−i−i−i−iii000000000000000
χ354444-4-4-4-44-21-2-211-212222-1-1-1-1-2-211-1-1220000002i−2i−2i2i00000000−i−iiiii−i−i0000000
χ364444-4-4-4-44-21-2-211-212222-1-1-1-1-2-211-1-122000000−2i2i2i−2i00000000ii−i−i−i−iii0000000
χ3744-4-4004i−4i01-21-12-2-123i3i−3i−3i2i2i−2i−2i3-30000i−i0000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000
χ3844-4-4004i−4i01-21-12-2-123i3i−3i−3i2i2i−2i−2i3-30000i−i0000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000
χ3944-4-4004i−4i01-21-12-2-12−3i−3i3i3i2i2i−2i−2i-330000i−i0000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000
χ4044-4-4004i−4i01-21-12-2-12−3i−3i3i3i2i2i−2i−2i-330000i−i0000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000
χ4144-4-4004i−4i0444-4-44-4-40000−4i−4i4i4i0000004i−4i000000000000000000000000000000000
χ4244-4-400−4i4i01-21-12-2-123i3i−3i−3i−2i−2i2i2i-330000−ii0000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000
χ4344-4-400−4i4i01-21-12-2-123i3i−3i−3i−2i−2i2i2i-330000−ii0000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000
χ4444-4-400−4i4i01-21-12-2-12−3i−3i3i3i−2i−2i2i2i3-30000−ii0000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000
χ4544-4-400−4i4i01-21-12-2-12−3i−3i3i3i−2i−2i2i2i3-30000−ii0000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000
χ4644-4-400−4i4i0444-4-44-4-400004i4i−4i−4i000000−4i4i000000000000000000000000000000000
χ474-44-44i−4i00044-444-4-4-44i−4i4i−4i000000004i−4i00000000000000000000000000000000000
χ484-44-44i−4i000-212-21-12-1−2i2i−2i2i3i−3i3i−3i003-3i−i00000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000
χ494-44-44i−4i000-212-21-12-1−2i2i−2i2i3i−3i3i−3i003-3i−i00000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000
χ504-44-44i−4i000-212-21-12-1−2i2i−2i2i−3i3i−3i3i00-33i−i00000000000000000000−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000
χ514-44-44i−4i000-212-21-12-1−2i2i−2i2i−3i3i−3i3i00-33i−i00000000000000000000ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000
χ524-44-4−4i4i00044-444-4-4-4−4i4i−4i4i00000000−4i4i00000000000000000000000000000000000
χ534-44-4−4i4i000-212-21-12-12i−2i2i−2i3i−3i3i−3i00-33−ii00000000000000000000ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ130000000
χ544-44-4−4i4i000-212-21-12-12i−2i2i−2i3i−3i3i−3i00-33−ii00000000000000000000−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000
χ554-44-4−4i4i000-212-21-12-12i−2i2i−2i−3i3i−3i3i003-3−ii00000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000
χ564-44-4−4i4i000-212-21-12-12i−2i2i−2i−3i3i−3i3i003-3−ii00000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000
χ574-4-440000044-4-4-4-44400000000000000004-40000000000000000000000000000000
χ584-4-440000044-4-4-4-4440000000000000000-440000000000000000000000000000000
χ5988-8-8008i−8i0-42-44-224-20000−2i−2i2i2i000000−4i4i000000000000000000000000000000000
χ6088-8-800−8i8i0-42-44-224-200002i2i−2i−2i0000004i−4i000000000000000000000000000000000
χ618-88-88i−8i0002-4-22-44-242i−2i2i−2i00000000−4i4i00000000000000000000000000000000000
χ628-88-8−8i8i0002-4-22-44-24−2i2i−2i2i000000004i−4i00000000000000000000000000000000000
χ638-8-88000002-4-2-2442-46-6-66000000000000000000000000000000000000000000000
χ648-8-88000002-4-2-2442-4-666-6000000000000000000000000000000000000000000000
χ658-8-8800000-4244-2-2-4200006-6-6600000000000000000000000000000000000000000
χ668-8-8800000-4244-2-2-420000-666-600000000000000000000000000000000000000000

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