Finite Group Databasebeta

← Group #11772587

Character table — Group #11772587

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size1124444444888888889916161616161616161616161618363636363636367272727272727272
order122223346666881212121244666624242424242424244244888888888888
χ1111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111-1-1111111111111-1-1-1-1ii−i−i-1-1i−iii−i−i
χ4111111111111111111-1-1111111111111-1-1-1-1−i−iii-1-1−ii−i−iii
χ5111111111111-1-11111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1
χ6111111111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ7111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i11i−i−i−iii
χ8111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii11−iiii−i−i
χ91111-111-11111i−i-1-1-1-11111-1-1iiii−i−i−i−i1-11-11111i−i-1-1i−ii−i
χ101111-111-11111i−i-1-1-1-11111-1-1iiii−i−i−i−i1-11-1-1-1-1-1i−i11−ii−ii
χ111111-111-11111i−i-1-1-1-1-1-111-1-1iiii−i−i−i−i-11-11ii−i−i−ii−ii-111-1
χ121111-111-11111i−i-1-1-1-1-1-111-1-1iiii−i−i−i−i-11-11−i−iii−iii−i1-1-11
χ131111-111-11111−ii-1-1-1-11111-1-1−i−i−i−iiiii1-11-11111−ii-1-1−ii−ii
χ141111-111-11111−ii-1-1-1-11111-1-1−i−i−i−iiiii1-11-1-1-1-1-1−ii11i−ii−i
χ151111-111-11111−ii-1-1-1-1-1-111-1-1−i−i−i−iiiii-11-11ii−i−ii−i−ii1-1-11
χ161111-111-11111−ii-1-1-1-1-1-111-1-1−i−i−i−iiiii-11-11−i−iiii−ii−i-111-1
χ17222-2222-2222200-2-2-2-222-2-222000000002-2-22000000000000
χ18222-2222-2222200-2-2-2-2-2-2-2-22200000000-222-2000000000000
χ19222-2-2222222200222222-2-2-2-20000000022-2-2000000000000
χ20222-2-22222222002222-2-2-2-2-2-200000000-2-222000000000000
χ21444441-241-21-24411-2-2001-21-211-2-211-2-20000000000000000
χ22444441-241-21-2-4-411-2-2001-21-2-1-122-1-1220000000000000000
χ2344444-214-21-2144-2-21100-21-21-2-211-2-2110000000000000000
χ2444444-214-21-21-4-4-2-21100-21-2122-1-122-1-10000000000000000
χ254444-41-2-41-21-24i−4i-1-122001-2-12ii−2i−2i−i−i2i2i0000000000000000
χ264444-41-2-41-21-2−4i4i-1-122001-2-12−i−i2i2iii−2i−2i0000000000000000
χ274444-4-21-4-21-214i−4i22-1-100-212-1−2i−2iii2i2i−i−i0000000000000000
χ284444-4-21-4-21-21−4i4i22-1-100-212-12i2i−i−i−2i−2iii0000000000000000
χ29444-441-2-41-21-200-1-12200-121-23i−3i003i−3i000000000000000000
χ30444-441-2-41-21-200-1-12200-121-2−3i3i00−3i3i000000000000000000
χ31444-44-21-4-21-210022-1-1002-1-21003i−3i003i−3i0000000000000000
χ32444-44-21-4-21-210022-1-1002-1-2100−3i3i00−3i3i0000000000000000
χ33444-4-41-241-21-20011-2-200-12-123-300-33000000000000000000
χ34444-4-41-241-21-20011-2-200-12-12-33003-3000000000000000000
χ35444-4-4-214-21-2100-2-211002-12-1003-300-330000000000000000
χ36444-4-4-214-21-2100-2-211002-12-100-33003-30000000000000000
χ3744-40044044-4-400000044000000000000-4000000000000000
χ3844-40044044-4-4000000-4-40000000000004000000000000000
χ394-4000440-4-4000000004i−4i00000000000000002ζ−2ζ2ζ3−2ζ300000000
χ404-4000440-4-4000000004i−4i0000000000000000−2ζ2ζ−2ζ32ζ300000000
χ414-4000440-4-400000000−4i4i00000000000000002ζ3−2ζ32ζ−2ζ00000000
χ424-4000440-4-400000000−4i4i0000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ4388-8002-402-4-24006-600000000000000000000000000000000
χ4488-8002-402-4-2400-6600000000000000000000000000000000
χ4588-800-420-424-200006-6000000000000000000000000000000
χ4688-800-420-424-20000-66000000000000000000000000000000
χ4716-160004-80-4800000000000000000000000000000000000000
χ4816-16000-8408-400000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.