Finite Group Databasebeta

← Group #263387

Character table — Group #263387

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11112222224444444488888888888888161616161616161616161616161632323232
order12222244444444888822224444888888244444444488888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111-1-111-1-1111111111-1-11-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111-1-111-1-1111111-1-1-111-111-1-1-1-1-1-1-1-111
χ5111111111111111111-1-111-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1
χ6111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-11-1-11111-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1111111-1-111-1-1
χ911111111111111-1-1-1-111111111-1-1-1-1-1-111-11-1-11-111-1-1-1-11-11-1
χ1011111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1111-1-1-1-1-11-11
χ1111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-11-1-11-1-111111-1-11
χ1211111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-111-1-1-11111-111-1
χ1311111111111111-1-1-1-1-1-111-1-111-1-1111111-11-1-11-1-1-111-1-1-11-11
χ1411111111111111-1-1-1-1-1-111-1-111-1-11111-1-11-111-11-1-111-1-11-11-1
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-111-111-1
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-111-111-1-1111-1-11
χ172222222222-2-2-2-22222002-2002-2-2-200000000000000002-20000
χ182222222222-2-2-2-2222200-2200-22-2-20000000000000000-220000
χ192222222222-2-2-2-2-2-2-2-2002-2002-2220000000000000000-220000
χ202222222222-2-2-2-2-2-2-2-200-2200-222200000000000000002-20000
χ21222222-2-2-2-222-2-20000002200-2-2002i2i−2i−2i00000000002i−2i000000
χ22222222-2-2-2-222-2-20000002200-2-200−2i−2i2i2i0000000000−2i2i000000
χ23222222-2-2-2-222-2-2000000-2-20022002i2i−2i−2i0000000000−2i2i000000
χ24222222-2-2-2-222-2-2000000-2-2002200−2i−2i2i2i00000000002i−2i000000
χ25222222-2-2-2-2-2-2220000222-2-2-2-22000000000000002-200000000
χ26222222-2-2-2-2-2-222000022-22-2-22-200000000000000-2200000000
χ27222222-2-2-2-2-2-2220000-2-22-222-2200000000000000-2200000000
χ28222222-2-2-2-2-2-2220000-2-2-22222-2000000000000002-200000000
χ292222-2-2-2-2222-22-222-2-2000000002-20000000220-2-20000000000
χ302222-2-2-2-2222-22-222-2-2000000002-20000000-2-20220000000000
χ312222-2-2-2-2222-22-2-2-22200000000-2200000002-20-220000000000
χ322222-2-2-2-2222-22-2-2-22200000000-220000000-2202-20000000000
χ332222-2-2-2-222-22-2222-2-200000000-2200002-2200-2000000000000
χ342222-2-2-2-222-22-2222-2-200000000-220000-22-2002000000000000
χ352222-2-2-2-222-22-22-2-222000000002-200002-2-2002000000000000
χ362222-2-2-2-222-22-22-2-222000000002-20000-22200-2000000000000
χ374444-4-444-4-44-4-44000000000000000000000000000000000000
χ384444-4-444-4-4-444-4000000000000000000000000000000000000
χ394-44-4004i−4i00000022−222i2−2i22-2002i−2i00002ζ−2ζ2ζ3−2ζ3000000000000000000
χ404-44-4004i−4i00000022−222i2−2i2-2200−2i2i0000−2ζ2ζ−2ζ32ζ3000000000000000000
χ414-44-4004i−4i000000−2222−2i22i22-2002i−2i0000−2ζ2ζ−2ζ32ζ3000000000000000000
χ424-44-4004i−4i000000−2222−2i22i2-2200−2i2i00002ζ−2ζ2ζ3−2ζ3000000000000000000
χ434-44-400−4i4i00000022−22−2i22i22-200−2i2i0000−2ζ32ζ3−2ζ2ζ000000000000000000
χ444-44-400−4i4i00000022−22−2i22i2-22002i−2i00002ζ3−2ζ32ζ−2ζ000000000000000000
χ454-44-400−4i4i000000−22222i2−2i22-200−2i2i00002ζ3−2ζ32ζ−2ζ000000000000000000
χ464-44-400−4i4i000000−22222i2−2i2-22002i−2i0000−2ζ32ζ3−2ζ2ζ000000000000000000
χ4788-8-88-800000000000000000000000000000000000000000000
χ4888-8-8-8800000000000000000000000000000000000000000000
χ498-8-8800008-80000000000000000000000000000000000000000
χ508-8-880000-880000000000000000000000000000000000000000

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