Finite Group Databasebeta

← Group #11772635

Character table — Group #11772635

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size1124444444888888889916161616161616161616161618363636363636367272727272727272
order1223344466668812121212441212121224242424242424244222888844448888
χ1111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1
χ3111111111111111111-1-1111111111111-1-1-1-1ii−i−iii−i−i-1-1i−i
χ4111111111111111111-1-1111111111111-1-1-1-1−i−iii−i−iii-1-1−ii
χ5111111111111-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ6111111111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ7111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iii11i−i
χ8111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i11−ii
χ9111111-1-11111i−i-1-1-1-11111-1-1iiii−i−i−i−i11-1-11111i−ii−ii−i-1-1
χ10111111-1-11111i−i-1-1-1-11111-1-1iiii−i−i−i−i11-1-1-1-1-1-1−ii−iii−i11
χ11111111-1-11111i−i-1-1-1-1-1-111-1-1iiii−i−i−i−i-1-111ii−i−i-111-1−ii−ii
χ12111111-1-11111i−i-1-1-1-1-1-111-1-1iiii−i−i−i−i-1-111−i−iii1-1-11−iii−i
χ13111111-1-11111−ii-1-1-1-11111-1-1−i−i−i−iiiii11-1-11111−ii−ii−ii-1-1
χ14111111-1-11111−ii-1-1-1-11111-1-1−i−i−i−iiiii11-1-1-1-1-1-1i−ii−i−ii11
χ15111111-1-11111−ii-1-1-1-1-1-111-1-1−i−i−i−iiiii-1-111ii−i−i1-1-11i−i−ii
χ16111111-1-11111−ii-1-1-1-1-1-111-1-1−i−i−i−iiiii-1-111−i−iii-111-1i−ii−i
χ1722222-22-2222200-2-2-2-222-2-222000000002-2-22000000000000
χ1822222-22-2222200-2-2-2-2-2-2-2-22200000000-222-2000000000000
χ1922222-2-22222200222222-2-2-2-2000000002-22-2000000000000
χ2022222-2-222222002222-2-2-2-2-2-200000000-22-22000000000000
χ214441-24441-21-24411-2-2001-21-211-2-211-2-20000000000000000
χ224441-24441-21-2-4-411-2-2001-21-2-1-122-1-1220000000000000000
χ234441-24-4-41-21-24i−4i-1-122001-2-12ii−2i−2i−i−i2i2i0000000000000000
χ244441-24-4-41-21-2−4i4i-1-122001-2-12−i−i2i2iii−2i−2i0000000000000000
χ254441-2-44-41-21-200-1-12200-121-23i−3i003i−3i000000000000000000
χ264441-2-44-41-21-200-1-12200-121-2−3i3i00−3i3i000000000000000000
χ274441-2-4-441-21-20011-2-200-12-123-300-33000000000000000000
χ284441-2-4-441-21-20011-2-200-12-12-33003-3000000000000000000
χ29444-21444-21-2144-2-21100-21-21-2-211-2-2110000000000000000
χ30444-21444-21-21-4-4-2-21100-21-2122-1-122-1-10000000000000000
χ31444-214-4-4-21-214i−4i22-1-100-212-1−2i−2iii2i2i−i−i0000000000000000
χ32444-214-4-4-21-21−4i4i22-1-100-212-12i2i−i−i−2i−2iii0000000000000000
χ33444-21-44-4-21-210022-1-1002-1-21003i−3i003i−3i0000000000000000
χ34444-21-44-4-21-210022-1-1002-1-2100−3i3i00−3i3i0000000000000000
χ35444-21-4-44-21-2100-2-211002-12-1003-300-330000000000000000
χ36444-21-4-44-21-2100-2-211002-12-100-33003-30000000000000000
χ3744-44400044-4-400000044000000000000-4000000000000000
χ3844-44400044-4-4000000-4-40000000000004000000000000000
χ394-4044000-4-4000000004i−4i00000000000000002ζ−2ζ2ζ3−2ζ300000000
χ404-4044000-4-4000000004i−4i0000000000000000−2ζ2ζ−2ζ32ζ300000000
χ414-4044000-4-400000000−4i4i00000000000000002ζ3−2ζ32ζ−2ζ00000000
χ424-4044000-4-400000000−4i4i0000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ4388-82-40002-4-24006-600000000000000000000000000000000
χ4488-82-40002-4-2400-6600000000000000000000000000000000
χ4588-8-42000-424-200006-6000000000000000000000000000000
χ4688-8-42000-424-20000-66000000000000000000000000000000
χ4716-1604-8000-4800000000000000000000000000000000000000
χ4816-160-840008-400000000000000000000000000000000000000

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