Finite Group Databasebeta

← Group #11771237

Character table — Group #11771237

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
χ5111111-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-1ii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-111-1ii−i−i
χ6111111-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-1ii−i−i-1-111iiii−i−i−i−i-1-1-1-1111111-1−i−iii
χ7111111-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-1−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-111-1−i−iii
χ8111111-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-1−i−iii-1-111−i−i−i−iiiii-1-1-1-1111111-1ii−i−i
χ91111-1-111-111111111-1-11111-1-1-1-1-1-1-1-111-1-11-11-1i−ii−i11-1-111-1-1ii−i−iii−i−i1-11i−ii−i
χ101111-1-111-111111111-1-11111-1-1-1-1-1-1-1-111-1-11-11-1−ii−ii11-1-111-1-1−i−iii−i−iii1-11−ii−ii
χ111111-1-111-111111111-1-11111-1-1-1-1-1-1-1-111-1-1-11-11i−ii−i-1-111-1-111ii−i−iii−i−i1-11−ii−ii
χ121111-1-111-111111111-1-11111-1-1-1-1-1-1-1-111-1-1-11-11−ii−ii-1-111-1-111−i−iii−i−iii1-11i−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
χ18222222-2-2-22222222222-2-2-2-222-2-2-2-222-2-222000000000000000000000000-2-220000
χ192222-2-222-222222222-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000-22-20000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000000000000-2220000
χ214444444441-211-2-21-211-2-2-2-21111-2-2-2-211000000222200000000-1-1-1-1-1-1-1-10000000
χ224444444441-211-2-21-211-2-2-2-21111-2-2-2-211000000-2-2-2-200000000111111110000000
χ23444444444-21-2-211-21-2-21111-2-2-2-21111-2-20022220000-1-1-1-1-1-1-1-1000000000000000
χ24444444444-21-2-211-21-2-21111-2-2-2-21111-2-200-2-2-2-2000011111111000000000000000
χ25444444-4-4-41-211-2-21-211222211-1-122-2-2-1-100000022-2-200000000-1-1-1-111110000000
χ26444444-4-4-41-211-2-21-211222211-1-122-2-2-1-1000000-2-222000000001111-1-1-1-10000000
χ27444444-4-4-4-21-2-211-21-2-2-1-1-1-1-2-222-1-11122002i2i−2i−2i0000−i−i−i−iiiii000000000000000
χ28444444-4-4-4-21-2-211-21-2-2-1-1-1-1-2-222-1-1112200−2i−2i2i2i0000iiii−i−i−i−i000000000000000
χ294444-4-444-41-211-2-21-2-1-1-2-2-2-2-1-1-1-12222110000002i−2i2i−2i00000000−i−iii−i−iii0000000
χ304444-4-444-41-211-2-21-2-1-1-2-2-2-2-1-1-1-1222211000000−2i2i−2i2i00000000ii−i−iii−i−i0000000
χ314444-4-444-4-21-2-211-212211112222-1-1-1-1-2-2002-22-20000-1-111-1-111000000000000000
χ324444-4-444-4-21-2-211-212211112222-1-1-1-1-2-200-22-22000011-1-111-1-1000000000000000
χ334444-4-4-4-441-211-2-21-2-1-12222-1-111-2-222-1-10000002i−2i−2i2i00000000−i−iiiii−i−i0000000
χ344444-4-4-4-441-211-2-21-2-1-12222-1-111-2-222-1-1000000−2i2i2i−2i00000000ii−i−i−i−iii0000000
χ354444-4-4-4-44-21-2-211-2122-1-1-1-122-2-211-1-122002i−2i−2i2i0000−i−iiiii−i−i000000000000000
χ364444-4-4-4-44-21-2-211-2122-1-1-1-122-2-211-1-12200−2i2i2i−2i0000ii−i−i−i−iii000000000000000
χ3744-4-400000444-44-4-4-400000000000000004-40000000000000000000000000000000
χ3844-4-400000444-44-4-4-40000000000000000-440000000000000000000000000000000
χ394-44-44i−4i00044-44-44-4-44i−4i00004i−4i00004i−4i00000000000000000000000000000000000
χ404-44-44i−4i000-212-2-112-1−2i2i3i3i−3i−3i−2i2i003-3i−i000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000
χ414-44-44i−4i000-212-2-112-1−2i2i3i3i−3i−3i−2i2i003-3i−i000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000
χ424-44-44i−4i000-212-2-112-1−2i2i−3i−3i3i3i−2i2i00-33i−i000000000000−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000
χ434-44-44i−4i000-212-2-112-1−2i2i−3i−3i3i3i−2i2i00-33i−i000000000000ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000
χ444-44-4−4i4i00044-44-44-4-4−4i4i0000−4i4i0000−4i4i00000000000000000000000000000000000
χ454-44-4−4i4i000-212-2-112-12i−2i3i3i−3i−3i2i−2i00-33−ii000000000000ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000
χ464-44-4−4i4i000-212-2-112-12i−2i3i3i−3i−3i2i−2i00-33−ii000000000000−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000
χ474-44-4−4i4i000-212-2-112-12i−2i−3i−3i3i3i2i−2i003-3−ii000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000
χ484-44-4−4i4i000-212-2-112-12i−2i−3i−3i3i3i2i−2i003-3−ii000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000
χ494-4-44004-401-2-1-1221-2332-22-2-3-33-300001-1000000000000000000−i3i3−i3i3−i3i3−i3i30000000
χ504-4-44004-401-2-1-1221-2332-22-2-3-33-300001-1000000000000000000i3−i3i3−i3i3−i3i3−i30000000
χ514-4-44004-401-2-1-1221-2-3-32-22-233-3300001-10000000000000000003−3−333−3−330000000
χ524-4-44004-401-2-1-1221-2-3-32-22-233-3300001-1000000000000000000−333−3−333−30000000
χ534-4-44004-4044-4-4-4-44400-44-44000000004-4000000000000000000000000000000000
χ544-4-4400-4401-2-1-1221-233-22-22-3-3-330000-11000000000000000000−i3i3−i3i3i3−i3i3−i30000000
χ554-4-4400-4401-2-1-1221-233-22-22-3-3-330000-11000000000000000000i3−i3i3−i3−i3i3−i3i30000000
χ564-4-4400-4401-2-1-1221-2-3-3-22-22333-30000-110000000000000000003−3−33−333−30000000
χ574-4-4400-4401-2-1-1221-2-3-3-22-22333-30000-11000000000000000000−333−33−3−330000000
χ584-4-4400-44044-4-4-4-444004-44-400000000-44000000000000000000000000000000000
χ5988-8-8000002-42-2-44-246i−6i0000−6i6i00000000000000000000000000000000000000000
χ6088-8-8000002-42-2-44-24−6i6i00006i−6i00000000000000000000000000000000000000000
χ6188-8-800000-42-442-24-2006i−6i−6i6i0000000000000000000000000000000000000000000
χ6288-8-800000-42-442-24-200−6i6i6i−6i0000000000000000000000000000000000000000000
χ638-88-88i−8i0002-4-224-4-242i−2i00002i−2i0000−4i4i00000000000000000000000000000000000
χ648-88-8−8i8i0002-4-224-4-24−2i2i0000−2i2i00004i−4i00000000000000000000000000000000000
χ658-8-88008-80-4244-2-2-4200-22-2200000000-44000000000000000000000000000000000
χ668-8-8800-880-4244-2-2-42002-22-2000000004-4000000000000000000000000000000000

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