Finite Group Databasebeta

← Group #11777058

Character table — Group #11777058

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size1111222248888888888888888999918181818363636363636363636363636363636363672727272
order122244444366612121212121212121212121244444444288888888888888888888
χ1111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111-1-111-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111ii−i−iii−i−i11-1-111-1-1i−ii−i
χ101111-1-111-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111ii−i−iii−i−i-1-111-1-111−ii−ii
χ111111-1-111-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111−i−iii−i−iii11-1-111-1-1−ii−ii
χ121111-1-111-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111−i−iii−i−iii-1-111-1-111i−ii−i
χ131111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1ii−i−i−i−iii11-1-1-1-111i−i−ii
χ141111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1ii−i−i−i−iii-1-11111-1-1−iii−i
χ151111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1−i−iiiii−i−i11-1-1-1-111−iii−i
χ161111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1−i−iiiii−i−i-1-11111-1-1i−i−ii
χ172222222222222222222222222-2-2-2-2-2-2-2-2-200000000000000000000
χ18222222-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2200000000000000000000
χ192222-2-222-22222-2-2-2-22222-2-2-2-2222222-2-2-200000000000000000000
χ202222-2-2-2-222222-2-2-2-2-2-2-2-222222222-2-2-2-2200000000000000000000
χ2122-2-2002i−2i022-2-200002i2i−2i−2i000022-2-22i−2i00000000000i2−i2i2−i22−22−20000
χ2222-2-2002i−2i022-2-200002i2i−2i−2i000022-2-22i−2i00000000000−i2i2−i2i2−22−220000
χ2322-2-2002i−2i022-2-200002i2i−2i−2i0000-2-222−2i2i00000000000i2−i2−i2i22−2−220000
χ2422-2-2002i−2i022-2-200002i2i−2i−2i0000-2-222−2i2i00000000000−i2i2i2−i2−222−20000
χ2522-2-200−2i2i022-2-20000−2i−2i2i2i000022-2-2−2i2i00000000000i2−i2i2−i2−22−220000
χ2622-2-200−2i2i022-2-20000−2i−2i2i2i000022-2-2−2i2i00000000000−i2i2−i2i22−22−20000
χ2722-2-200−2i2i022-2-20000−2i−2i2i2i0000-2-2222i−2i00000000000i2−i2−i2i2−222−20000
χ2822-2-200−2i2i022-2-20000−2i−2i2i2i0000-2-2222i−2i00000000000−i2i2i2−i22−2−220000
χ292-22-22i−2i0002-22-22i2i−2i−2i000000002i−2i2i−2i002-2000002ζ−2ζ2ζ3−2ζ3000000000000
χ302-22-22i−2i0002-22-22i2i−2i−2i000000002i−2i2i−2i002-200000−2ζ2ζ−2ζ32ζ3000000000000
χ312-22-22i−2i0002-22-22i2i−2i−2i00000000−2i2i−2i2i00-2202ζ3−2ζ32ζ−2ζ0000000000000000
χ322-22-22i−2i0002-22-22i2i−2i−2i00000000−2i2i−2i2i00-220−2ζ32ζ3−2ζ2ζ0000000000000000
χ332-22-2−2i2i0002-22-2−2i−2i2i2i000000002i−2i2i−2i00-2202ζ−2ζ2ζ3−2ζ30000000000000000
χ342-22-2−2i2i0002-22-2−2i−2i2i2i000000002i−2i2i−2i00-220−2ζ2ζ−2ζ32ζ30000000000000000
χ352-22-2−2i2i0002-22-2−2i−2i2i2i00000000−2i2i−2i2i002-2000002ζ3−2ζ32ζ−2ζ000000000000
χ362-22-2−2i2i0002-22-2−2i−2i2i2i00000000−2i2i−2i2i002-200000−2ζ32ζ3−2ζ2ζ000000000000
χ374-4-44000004-4-440000000000004i−4i−4i4i0000000000000000000000000
χ384-4-44000004-4-44000000000000−4i4i4i−4i0000000000000000000000000
χ39888888888-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000
χ40888888-8-8-8-1-1-1-1-1-1-1-11111111100000000000000000000000000000
χ418888-8-888-8-1-1-1-11111-1-1-1-1111100000000000000000000000000000
χ428888-8-8-8-88-1-1-1-111111111-1-1-1-100000000000000000000000000000
χ4388-8-8008i−8i0-1-1113i−3i3i−3i−i−iii33-3-300000000000000000000000000000
χ4488-8-8008i−8i0-1-111−3i3i−3i3i−i−iii-3-33300000000000000000000000000000
χ4588-8-800−8i8i0-1-1113i−3i3i−3iii−i−i-3-33300000000000000000000000000000
χ4688-8-800−8i8i0-1-111−3i3i−3i3iii−i−i33-3-300000000000000000000000000000
χ478-88-88i−8i000-11-11−i−iii3-33-33i−3i3i−3i00000000000000000000000000000
χ488-88-88i−8i000-11-11−i−iii-33-33−3i3i−3i3i00000000000000000000000000000
χ498-88-8−8i8i000-11-11ii−i−i3-33-3−3i3i−3i3i00000000000000000000000000000
χ508-88-8−8i8i000-11-11ii−i−i-33-333i−3i3i−3i00000000000000000000000000000
χ518-8-8800000-111-13-3-333i−3i−3i3i−3i3i3i−3i00000000000000000000000000000
χ528-8-8800000-111-13-3-33−3i3i3i−3i3i−3i−3i3i00000000000000000000000000000
χ538-8-8800000-111-1-333-33i−3i−3i3i3i−3i−3i3i00000000000000000000000000000
χ548-8-8800000-111-1-333-3−3i3i3i−3i−3i3i3i−3i00000000000000000000000000000

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