Finite Group Databasebeta

← Group #150013

Character table — Group #150013

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41
size111122224448888888888816161616161616161616161616323232323232
order12222244444224444444444888888888888448888
χ111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111-1-111111-1-1-1-1-11111iiii−i−i−i−i-1-1ii−i−i
χ611111111111-1-111111-1-1-1-1-11111−i−i−i−iiiii-1-1−i−iii
χ711111111111-1-111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ811111111111-1-111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ9111111-1-11-1111-111-1-1-1-1-1-1111-1-1ii−i−iii−i−i1-1i−ii−i
χ10111111-1-11-1111-111-1-1-1-1-1-1111-1-1−i−iii−i−iii1-1−ii−ii
χ11111111-1-11-1111-111-1-1-1-1-1-11-1-111ii−i−iii−i−i-11−ii−ii
χ12111111-1-11-1111-111-1-1-1-1-1-11-1-111−i−iii−i−iii-11i−ii−i
χ13111111-1-11-11-1-1-111-1-11111-111-1-111-1-1-1-111-111-1-11
χ14111111-1-11-11-1-1-111-1-11111-111-1-1-1-11111-1-1-11-111-1
χ15111111-1-11-11-1-1-111-1-11111-1-1-11111-1-1-1-1111-1-111-1
χ16111111-1-11-11-1-1-111-1-11111-1-1-111-1-11111-1-11-11-1-11
χ1722222222222222-2-2-2-222-2-2-2000000000000000000
χ1822222222222-2-22-2-2-2-2-2-2222000000000000000000
χ19222222-2-22-2222-2-2-222-2-222-2000000000000000000
χ20222222-2-22-22-2-2-2-2-22222-2-22000000000000000000
χ2122-2-22-200-2020002-2002i−2i2i−2i00000002ζ3−2ζ32ζ−2ζ00000000
χ2222-2-22-200-2020002-2002i−2i2i−2i0000000−2ζ32ζ3−2ζ2ζ00000000
χ2322-2-22-200-2020002-200−2i2i−2i2i00000002ζ−2ζ2ζ3−2ζ300000000
χ2422-2-22-200-2020002-200−2i2i−2i2i0000000−2ζ2ζ−2ζ32ζ300000000
χ2522-2-22-200-202000-22002i−2i−2i2i000002ζ−2ζ00002ζ3−2ζ3000000
χ2622-2-22-200-202000-22002i−2i−2i2i00000−2ζ2ζ0000−2ζ32ζ3000000
χ2722-2-22-200-202000-2200−2i2i2i−2i000002ζ3−2ζ300002ζ−2ζ000000
χ2822-2-22-200-202000-2200−2i2i2i−2i00000−2ζ32ζ30000−2ζ2ζ000000
χ2944444444-44-400-4000000000000000000000000000
χ30444444-4-4-4-4-4004000000000000000000000000000
χ314444-4-4440-400000000000002-22-200000000000000
χ324444-4-4440-40000000000000-22-2200000000000000
χ334444-4-4-4-40400000000000002-2-2200000000000000
χ344444-4-4-4-4040000000000000-222-200000000000000
χ3544-4-44-40040-44-40000000000000000000000000000
χ3644-4-44-40040-4-440000000000000000000000000000
χ3788-8-8-8800000000000000000000000000000000000
χ388-88-80000000000004i−4i00000000000000000000000
χ398-88-8000000000000−4i4i00000000000000000000000
χ408-8-88008i−8i000000000000000000000000000000000
χ418-8-8800−8i8i000000000000000000000000000000000

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