Finite Group Databasebeta

← Group #11771264

Character table — Group #11771264

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122224444444444444444488888888181824242424242424242424242424242424242424242424242436363672727272
order12224444334666666121212121212121212121212121212124488888888242424242424242424242424242424242448888
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
χ511111-1-1111-111111111-1-111-1-111-1-1-1-1-1-1-1-1ii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-111-1ii−i−i
χ611111-1-1111-111111111-1-111-1-111-1-1-1-1-1-1-1-1ii−i−i-1-111iiii−i−i−i−i-1-1-1-1111111-1−i−iii
χ711111-1-1111-111111111-1-111-1-111-1-1-1-1-1-1-1-1−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-111-1−i−iii
χ811111-1-1111-111111111-1-111-1-111-1-1-1-1-1-1-1-1−i−iii-1-111−i−i−i−iiiii-1-1-1-1111111-1ii−i−i
χ91111-111-111-1111111-1-111-1-111-1-111-1-1-1-1-1-11-11-1i−ii−i11-1-111-1-1ii−i−iii−i−i1-11i−ii−i
χ101111-111-111-1111111-1-111-1-111-1-111-1-1-1-1-1-11-11-1−ii−ii11-1-111-1-1−i−iii−i−iii1-11−ii−ii
χ111111-111-111-1111111-1-111-1-111-1-111-1-1-1-1-1-1-11-11i−ii−i-1-111-1-111ii−i−iii−i−i1-11−ii−ii
χ121111-111-111-1111111-1-111-1-111-1-111-1-1-1-1-1-1-11-11−ii−ii-1-111-1-111−i−iii−i−iii1-11i−ii−i
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii1-1-1-111-1
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i1-1-11-1-11
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii1-1-11-1-11
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i1-1-1-111-1
χ17222222222222222222222222222222222-2-2000000000000000000000000-2-2-20000
χ1822222-2-2222-222222222-2-222-2-222-2-2-2-2-2-222000000000000000000000000-2-220000
χ192222-222-222-2222222-2-222-2-222-2-222-2-2-2-222000000000000000000000000-22-20000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2000000000000000000000000-2220000
χ21444444441-24111-2-2-211-2-211-2-2-2-21111-2-2000000222200000000-1-1-1-1-1-1-1-10000000
χ22444444441-24111-2-2-211-2-211-2-2-2-21111-2-2000000-2-2-2-200000000111111110000000
χ2344444444-214-2-2-2111-2-211-2-21111-2-2-2-2110022220000-1-1-1-1-1-1-1-1000000000000000
χ2444444444-214-2-2-2111-2-211-2-21111-2-2-2-21100-2-2-2-2000011111111000000000000000
χ2544444-4-441-2-4111-2-2-211221122-2-2-1-1-1-12200000022-2-200000000-1-1-1-111110000000
χ2644444-4-441-2-4111-2-2-211221122-2-2-1-1-1-122000000-2-222000000001111-1-1-1-10000000
χ2744444-4-44-21-4-2-2-2111-2-2-1-1-2-2-1-1112222-1-1002i2i−2i−2i0000−i−i−i−iiiii000000000000000
χ2844444-4-44-21-4-2-2-2111-2-2-1-1-2-2-1-1112222-1-100−2i−2i2i2i0000iiii−i−i−i−i000000000000000
χ294444-444-41-2-4111-2-2-2-1-1-2-2-1-1-2-22211-1-1220000002i−2i2i−2i00000000−i−iii−i−iii0000000
χ304444-444-41-2-4111-2-2-2-1-1-2-2-1-1-2-22211-1-122000000−2i2i−2i2i00000000ii−i−iii−i−i0000000
χ314444-444-4-21-4-2-2-211122112211-1-1-2-222-1-1002-22-20000-1-111-1-111000000000000000
χ324444-444-4-21-4-2-2-211122112211-1-1-2-222-1-100-22-22000011-1-111-1-1000000000000000
χ334444-4-4-4-41-24111-2-2-2-1-122-1-12222-1-111-2-20000002i−2i−2i2i00000000−i−iiiii−i−i0000000
χ344444-4-4-4-41-24111-2-2-2-1-122-1-12222-1-111-2-2000000−2i2i2i−2i00000000ii−i−i−i−iii0000000
χ354444-4-4-4-4-214-2-2-211122-1-122-1-1-1-122-2-211002i−2i−2i2i0000−i−iiiii−i−i000000000000000
χ364444-4-4-4-4-214-2-2-211122-1-122-1-1-1-122-2-21100−2i2i2i−2i0000ii−i−i−i−iii000000000000000
χ3744-4-400004404-4-44-4-400000000000000004i−4i0000000000000000000000000000000
χ3844-4-400004404-4-44-4-40000000000000000−4i4i0000000000000000000000000000000
χ394-44-404i−4i01-20-11-122-23i−3i2i−2i3i−3i2i−2i00i−i3-300000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000
χ404-44-404i−4i01-20-11-122-23i−3i2i−2i3i−3i2i−2i00i−i3-300000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000
χ414-44-404i−4i01-20-11-122-2−3i3i2i−2i−3i3i2i−2i00i−i-3300000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000
χ424-44-404i−4i01-20-11-122-2−3i3i2i−2i−3i3i2i−2i00i−i-3300000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000
χ434-44-404i−4i0440-44-4-4-4400−4i4i00−4i4i004i−4i0000000000000000000000000000000000000
χ444-44-40−4i4i01-20-11-122-23i−3i−2i2i3i−3i−2i2i00−ii-3300000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000
χ454-44-40−4i4i01-20-11-122-23i−3i−2i2i3i−3i−2i2i00−ii-3300000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000
χ464-44-40−4i4i01-20-11-122-2−3i3i−2i2i−3i3i−2i2i00−ii3-300000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000
χ474-44-40−4i4i01-20-11-122-2−3i3i−2i2i−3i3i−2i2i00−ii3-300000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000
χ484-44-40−4i4i0440-44-4-4-44004i−4i004i−4i00−4i4i0000000000000000000000000000000000000
χ494-4-44400-4440-4-44-44-44400-4-4004-4000000000000000000000000000000000000000
χ504-4-44400-4-21022-2-11-1-2-23i−3i22−3i3i1-100003i−3i0000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000
χ514-4-44400-4-21022-2-11-1-2-23i−3i22−3i3i1-100003i−3i0000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000000
χ524-4-44400-4-21022-2-11-1-2-2−3i3i223i−3i1-10000−3i3i0000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000000000000
χ534-4-44400-4-21022-2-11-1-2-2−3i3i223i−3i1-10000−3i3i0000000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000000000000
χ544-4-44-4004440-4-44-44-4-4-4004400-44000000000000000000000000000000000000000
χ554-4-44-4004-21022-2-11-1223i−3i-2-2−3i3i-110000−3i3i0000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000000
χ564-4-44-4004-21022-2-11-1223i−3i-2-2−3i3i-110000−3i3i0000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000000
χ574-4-44-4004-21022-2-11-122−3i3i-2-23i−3i-1100003i−3i0000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000000
χ584-4-44-4004-21022-2-11-122−3i3i-2-23i−3i-1100003i−3i0000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000000000
χ5988-8-800002-402-2-2-4446i−6i00−6i6i0000000000000000000000000000000000000000000
χ6088-8-800002-402-2-2-444−6i6i006i−6i0000000000000000000000000000000000000000000
χ6188-8-80000-420-4442-2-2006600-6-600000000000000000000000000000000000000000
χ6288-8-80000-420-4442-2-200-6-6006600000000000000000000000000000000000000000
χ638-88-808i−8i0-4204-44-2-2200−2i2i00−2i2i00−4i4i0000000000000000000000000000000000000
χ648-88-80−8i8i0-4204-44-2-22002i−2i002i−2i004i−4i0000000000000000000000000000000000000
χ658-8-88800-82-40-2-224-442200-2-200-44000000000000000000000000000000000000000
χ668-8-88-80082-40-2-224-44-2-20022004-4000000000000000000000000000000000000000

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