Finite Group Databasebeta

← Group #11771239

Character table — Group #11771239

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122224444444444444444488888888181824242424242424242424242424242424242424242424242436363672727272
order12222244334666666666612121212661212121212124444448888121212121212121224242424242424242248888
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
χ5111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1ii−i−i
χ6111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1−i−iii
χ7111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i11-1−i−iii
χ8111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii11-1ii−i−i
χ91111-1-11111-11111-1-111-1-11111-1-111-1-1-1-1-1-1i−ii−i1-11-1ii−i−iii−i−i11-1-111-1-11-11i−ii−i
χ101111-1-11111-11111-1-111-1-11111-1-111-1-1-1-1-1-1i−ii−i-11-11ii−i−iii−i−i-1-111-1-1111-11−ii−ii
χ111111-1-11111-11111-1-111-1-11111-1-111-1-1-1-1-1-1−ii−ii1-11-1−i−iii−i−iii11-1-111-1-11-11−ii−ii
χ121111-1-11111-11111-1-111-1-11111-1-111-1-1-1-1-1-1−ii−ii-11-11−i−iii−i−iii-1-111-1-1111-11i−ii−i
χ131111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1111111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii1-1-1-111-1
χ141111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1111111i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i1-1-11-1-11
χ151111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1111111−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii1-1-11-1-11
χ161111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1111111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i1-1-1-111-1
χ17222222222222222222222222222222222-2-2000000000000000000000000-2-2-20000
χ18222222-2-222-22222222222-2-2-2-222-2-2-2-2-2-222000000000000000000000000-2-220000
χ192222-2-22222-22222-2-222-2-22222-2-222-2-2-2-222000000000000000000000000-22-20000
χ202222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2000000000000000000000000-2220000
χ21444444441-2411-2-2111-211-2-2-2-2-2-21111-2-20022220000-1-1-1-1-1-1-1-1000000000000000
χ22444444441-2411-2-2111-211-2-2-2-2-2-21111-2-200-2-2-2-2000011111111000000000000000
χ2344444444-214-2-211-2-2-21-2-2111111-2-2-2-211000000222200000000-1-1-1-1-1-1-1-10000000
χ2444444444-214-2-211-2-2-21-2-2111111-2-2-2-211000000-2-2-2-200000000111111110000000
χ25444444-4-41-2-411-2-2111-2112222-2-2-1-1-1-1220022-2-20000-1-1-1-11111000000000000000
χ26444444-4-41-2-411-2-2111-2112222-2-2-1-1-1-12200-2-22200001111-1-1-1-1000000000000000
χ27444444-4-4-21-4-2-211-2-2-21-2-2-1-1-1-1112222-1-10000002i2i−2i−2i00000000−i−i−i−iiiii0000000
χ28444444-4-4-21-4-2-211-2-2-21-2-2-1-1-1-1112222-1-1000000−2i−2i2i2i00000000iiii−i−i−i−i0000000
χ294444-4-4441-2-411-2-2-1-11-2-1-1-2-2-2-22211-1-122002i−2i2i−2i0000−i−iii−i−iii000000000000000
χ304444-4-4441-2-411-2-2-1-11-2-1-1-2-2-2-22211-1-12200−2i2i−2i2i0000ii−i−iii−i−i000000000000000
χ314444-4-444-21-4-2-21122-21221111-1-1-2-222-1-10000002-22-200000000-1-111-1-1110000000
χ324444-4-444-21-4-2-21122-21221111-1-1-2-222-1-1000000-22-220000000011-1-111-1-10000000
χ334444-4-4-4-41-2411-2-2-1-11-2-1-1222222-1-111-2-2002i−2i−2i2i0000−i−iiiii−i−i000000000000000
χ344444-4-4-4-41-2411-2-2-1-11-2-1-1222222-1-111-2-200−2i2i2i−2i0000ii−i−i−i−iii000000000000000
χ354444-4-4-4-4-214-2-21122-2122-1-1-1-1-1-122-2-2110000002i−2i−2i2i00000000−i−iiiii−i−i0000000
χ364444-4-4-4-4-214-2-21122-2122-1-1-1-1-1-122-2-211000000−2i2i2i−2i00000000ii−i−i−i−iii0000000
χ3744-4-4004i−4i1-201-12-23-3-123-32i2i−2i−2i00i−i3i−3i000000000000−i3i3−i3i33−33−3000000000000000
χ3844-4-4004i−4i1-201-12-23-3-123-32i2i−2i−2i00i−i3i−3i000000000000i3−i3i3−i3−33−33000000000000000
χ3944-4-4004i−4i1-201-12-2-33-12-332i2i−2i−2i00i−i−3i3i0000000000003−3−33i3−i3−i3i3000000000000000
χ4044-4-4004i−4i1-201-12-2-33-12-332i2i−2i−2i00i−i−3i3i000000000000−333−3−i3i3i3−i3000000000000000
χ4144-4-4004i−4i4404-4-4400-4-400−4i−4i4i4i004i−4i0000000000000000000000000000000000000
χ4244-4-400−4i4i1-201-12-23-3-123-3−2i−2i2i2i00−ii−3i3i000000000000−i3i3−i3i3−33−33000000000000000
χ4344-4-400−4i4i1-201-12-23-3-123-3−2i−2i2i2i00−ii−3i3i000000000000i3−i3i3−i33−33−3000000000000000
χ4444-4-400−4i4i1-201-12-2-33-12-33−2i−2i2i2i00−ii3i−3i0000000000003−3−33−i3i3i3−i3000000000000000
χ4544-4-400−4i4i1-201-12-2-33-12-33−2i−2i2i2i00−ii3i−3i000000000000−333−3i3−i3−i3i3000000000000000
χ4644-4-400−4i4i4404-4-4400-4-4004i4i−4i−4i00−4i4i0000000000000000000000000000000000000
χ474-44-44-400440-444-444-4-4-4-400004-4000000000000000000000000000000000000000
χ484-44-44-400-2102-21-1-2-22-1223i−3i3i−3i1-100003i−3i000000000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000
χ494-44-44-400-2102-21-1-2-22-1223i−3i3i−3i1-100003i−3i000000000000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000
χ504-44-44-400-2102-21-1-2-22-122−3i3i−3i3i1-10000−3i3i000000000000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000
χ514-44-44-400-2102-21-1-2-22-122−3i3i−3i3i1-10000−3i3i000000000000000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000
χ524-44-4-4400440-444-4-4-4-4-4440000-44000000000000000000000000000000000000000
χ534-44-4-4400-2102-21-1222-1-2-23i−3i3i−3i-110000−3i3i000000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000
χ544-44-4-4400-2102-21-1222-1-2-23i−3i3i−3i-110000−3i3i000000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000000
χ554-44-4-4400-2102-21-1222-1-2-2−3i3i−3i3i-1100003i−3i000000000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000
χ564-44-4-4400-2102-21-1222-1-2-2−3i3i−3i3i-1100003i−3i000000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000
χ574-4-440000440-4-4-4-40044000000000000004-40000000000000000000000000000000
χ584-4-440000440-4-4-4-4004400000000000000-440000000000000000000000000000000
χ5988-8-8008i−8i-420-44-22004-200−2i−2i2i2i00−4i4i0000000000000000000000000000000000000
χ6088-8-800−8i8i-420-44-22004-2002i2i−2i−2i004i−4i0000000000000000000000000000000000000
χ618-88-88-8002-40-22-4422-24-2-20000-44000000000000000000000000000000000000000
χ628-88-8-88002-40-22-44-2-2-242200004-4000000000000000000000000000000000000000
χ638-8-8800002-40-2-2446-62-4-66000000000000000000000000000000000000000000000
χ648-8-8800002-40-2-244-662-46-6000000000000000000000000000000000000000000000
χ658-8-880000-42044-2-200-42006-6-6600000000000000000000000000000000000000000
χ668-8-880000-42044-2-200-4200-666-600000000000000000000000000000000000000000

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