Finite Group Databasebeta

← Group #149967

Character table — Group #149967

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41
size1111224444444488888881616161616161616161616161616323232323232
order12222244444444444444422444488888888888888
χ111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111-1-111-1-111111111-1-1-1-1-1-1
χ4111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111-1-1-1-11111-1-1-1-1111-111iiii−i−i−i−i-1-1ii−i−i
χ6111111111-1-1-1-11111-1-1-1-1111-111−i−i−i−iiiii-1-1−i−iii
χ7111111111-1-1-1-11111-1-1-1-1-1-11-1-1-1iiii−i−i−i−i11−i−iii
χ8111111111-1-1-1-11111-1-1-1-1-1-11-1-1-1−i−i−i−iiiii11ii−i−i
χ9111111-1-1111111-111-1-1111-1-1-11-111-1-111-1-11-11-11-1
χ10111111-1-1111111-111-1-1111-1-1-11-1-1-111-1-1111-1-11-11
χ11111111-1-1111111-111-1-111-11-1-1-1111-1-111-1-1-11-11-11
χ12111111-1-1111111-111-1-111-11-1-1-11-1-111-1-111-111-11-1
χ13111111-1-11-1-1-1-11-11111-1-11-1-111-1ii−i−i−i−iii-11i−i−ii
χ14111111-1-11-1-1-1-11-11111-1-11-1-111-1−i−iiiii−i−i-11−iii−i
χ15111111-1-11-1-1-1-11-11111-1-1-11-11-11ii−i−i−i−iii1-1−iii−i
χ16111111-1-11-1-1-1-11-11111-1-1-11-11-11−i−iiiii−i−i1-1i−i−ii
χ17222222222222222-2-222-2-200-2-20000000000000000
χ18222222222-2-2-2-222-2-2-2-22200-220000000000000000
χ19222222-2-2222222-2-2-2-2-2-2-200220000000000000000
χ20222222-2-22-2-2-2-22-2-2-22222002-20000000000000000
χ212-2-222-20022i2i−2i−2i-202-2002i−2i000000002ζ3−2ζ3002ζ−2ζ000000
χ222-2-222-20022i2i−2i−2i-202-2002i−2i00000000−2ζ32ζ300−2ζ2ζ000000
χ232-2-222-20022i2i−2i−2i-20-2200−2i2i0000002ζ−2ζ002ζ3−2ζ300000000
χ242-2-222-20022i2i−2i−2i-20-2200−2i2i000000−2ζ2ζ00−2ζ32ζ300000000
χ252-2-222-2002−2i−2i2i2i-202-200−2i2i000000002ζ−2ζ002ζ3−2ζ3000000
χ262-2-222-2002−2i−2i2i2i-202-200−2i2i00000000−2ζ2ζ00−2ζ32ζ3000000
χ272-2-222-2002−2i−2i2i2i-20-22002i−2i0000002ζ3−2ζ3002ζ−2ζ00000000
χ282-2-222-2002−2i−2i2i2i-20-22002i−2i000000−2ζ32ζ300−2ζ2ζ00000000
χ2944444444-40000-4-400000000000000000000000000
χ30444444-4-4-40000-4400000000000000000000000000
χ314444-4-44-400000000000002200-2-200000000000000
χ324444-4-44-40000000000000-2-2002200000000000000
χ334444-4-4-4400000000000002-200-2200000000000000
χ344444-4-4-440000000000000-22002-200000000000000
χ354-4-444-400-4000040004-40000000000000000000000
χ364-4-444-400-400004000-440000000000000000000000
χ3788-8-8000004-44-40000000000000000000000000000
χ3888-8-800000-44-440000000000000000000000000000
χ398-88-8000004i−4i−4i4i0000000000000000000000000000
χ408-88-800000−4i4i4i−4i0000000000000000000000000000
χ418-8-88-8800000000000000000000000000000000000

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