Finite Group Databasebeta

← Group #11772639

Character table — Group #11772639

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size112444444488888899161616161824242424242424243636363636363648484848484848487272
order12222334666666121244666124444488882448888121212122424242488
χ1111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111
χ51111-111-11111-1-1-1-11111-1-11ii−i−iii−i−i-11-11111ii−i−iii−i−i-1-1
χ61111-111-11111-1-1-1-11111-1-11ii−i−i−i−iii-11-1-1-1-1-1ii−i−i−i−iii11
χ71111-111-11111-1-1-1-11111-1-11−i−iiiii−i−i-11-1-1-1-1-1−i−iiiii−i−i11
χ81111-111-11111-1-1-1-11111-1-11−i−iii−i−iii-11-11111−i−iii−i−iii-1-1
χ9111-1111-1111111-1-1-1-1-1-11-1-11-11-1i−ii−i11-1ii−i−i1-11-1i−ii−ii−i
χ10111-1111-1111111-1-1-1-1-1-11-1-11-11-1−ii−ii11-1−i−iii1-11-1−ii−ii−ii
χ11111-1111-1111111-1-1-1-1-1-11-1-1-11-11i−ii−i11-1−i−iii-11-11i−ii−i−ii
χ12111-1111-1111111-1-1-1-1-1-11-1-1-11-11−ii−ii11-1ii−i−i-11-11−ii−iii−i
χ13111-1-11111111-1-111-1-1-1-1-11-1i−i−ii1-1-11-111−i−iiii−i−ii1-1-11i−i
χ14111-1-11111111-1-111-1-1-1-1-11-1i−i−ii-111-1-111ii−i−ii−i−ii-111-1−ii
χ15111-1-11111111-1-111-1-1-1-1-11-1−iii−i1-1-11-111ii−i−i−iii−i1-1-11−ii
χ16111-1-11111111-1-111-1-1-1-1-11-1−iii−i-111-1-111−i−iii−iii−i-111-1i−i
χ172222222222222222-2-22222-200000000-2-2-200000000000000
χ182222-222-22222-2-2-2-2-2-222-2-2-2000000002-2200000000000000
χ19222-2222-2222222-2-222-2-22-2200000000-2-2200000000000000
χ20222-2-22222222-2-22222-2-2-222000000002-2-200000000000000
χ21444441-241-21-211-2-2001-2-210222200000000000-1-1-1-1000000
χ22444441-241-21-211-2-2001-2-210-2-2-2-2000000000001111000000
χ2344444-214-21-21-2-21100-211-200000222200000000000-1-1-1-100
χ2444444-214-21-21-2-21100-211-200000-2-2-2-200000000000111100
χ254444-41-2-41-21-2-1-122001-22-102i2i−2i−2i00000000000−i−iii000000
χ264444-41-2-41-21-2-1-122001-22-10−2i−2i2i2i00000000000ii−i−i000000
χ274444-4-21-4-21-2122-1-100-21-12000002i2i−2i−2i00000000000−i−iii00
χ284444-4-21-4-21-2122-1-100-21-1200000−2i−2i2i2i00000000000ii−i−i00
χ29444-441-2-41-21-2112200-12-2-102-22-200000000000-11-11000000
χ30444-441-2-41-21-2112200-12-2-10-22-22000000000001-11-1000000
χ31444-44-21-4-21-21-2-2-1-1002-112000002i−2i2i−2i00000000000−ii−ii00
χ32444-44-21-4-21-21-2-2-1-1002-11200000−2i2i−2i2i00000000000i−ii−i00
χ33444-4-41-241-21-2-1-1-2-200-122102i−2i−2i2i00000000000−iii−i000000
χ34444-4-41-241-21-2-1-1-2-200-12210−2i2i2i−2i00000000000i−i−ii000000
χ35444-4-4-214-21-212211002-1-1-2000002-2-2200000000000-111-100
χ36444-4-4-214-21-212211002-1-1-200000-222-2000000000001-1-1100
χ3744-40044044-4-40000440000-40000000000000000000000000
χ3844-40044044-4-40000-4-4000040000000000000000000000000
χ394-4000440-4-40000004i−4i00000000000000002ζ−2ζ2ζ3−2ζ30000000000
χ404-4000440-4-40000004i−4i0000000000000000−2ζ2ζ−2ζ32ζ30000000000
χ414-4000440-4-4000000−4i4i00000000000000002ζ3−2ζ32ζ−2ζ0000000000
χ424-4000440-4-4000000−4i4i0000000000000000−2ζ32ζ3−2ζ2ζ0000000000
χ4388-8002-402-4-246-60000000000000000000000000000000000
χ4488-8002-402-4-24-660000000000000000000000000000000000
χ4588-800-420-424-2006-600000000000000000000000000000000
χ4688-800-420-424-200-6600000000000000000000000000000000
χ4716-160004-80-4800000000000000000000000000000000000000
χ4816-16000-8408-400000000000000000000000000000000000000

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