Finite Group Databasebeta

← Group #130243

Character table — Group #130243

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11112222444444444448888888888888161616161616161616161616161632323232
order12224444222448888882444816161616161616162444444488161616168888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111111111111-1-1-1-1111111111111-1-11-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111-1-1-1-1111111111-1-1-111-111-1-1-1-1-1-1-1-111
χ71111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111-1-111
χ81111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-111-111-1-1111111-1-1
χ911111-1-111-1-11-111-1-1-1-11-1-111iiii−i−i−i−i11-11-1-11-11-1ii−i−ii−ii−i
χ1011111-1-111-1-11-111-1-1-1-11-1-111iiii−i−i−i−i-1-11-111-111-1ii−i−i−ii−ii
χ1111111-1-111-1-11-111-1-1-1-11-1-111−i−i−i−iiiii11-11-1-11-11-1−i−iii−ii−ii
χ1211111-1-111-1-11-111-1-1-1-11-1-111−i−i−i−iiiii-1-11-111-111-1−i−iiii−ii−i
χ1311111-1-111-1-11-111-1-1-1-1-111-11iiii−i−i−i−i11-1-11-1-11-11−i−iiii−i−ii
χ1411111-1-111-1-11-111-1-1-1-1-111-11iiii−i−i−i−i-1-111-111-1-11−i−iii−iii−i
χ1511111-1-111-1-11-111-1-1-1-1-111-11−i−i−i−iiiii11-1-11-1-11-11ii−i−i−iii−i
χ1611111-1-111-1-11-111-1-1-1-1-111-11−i−i−i−iiiii-1-111-111-1-11ii−i−ii−i−ii
χ172222222222222-2-2-2-2-2-22222-20000000000000000-2-200000000
χ182222222222222-2-2-2-2-2-2-2-2-2-2-200000000000000002200000000
χ1922222222-22-2-2-2222-2-220000-2000000002-2-2002000000000000
χ2022222222-22-2-2-2222-2-220000-200000000-22200-2000000000000
χ2122222222-22-2-2-2-2-2-222-200002000000000002-20-220000000000
χ2222222222-22-2-2-2-2-2-222-20000200000000000-2202-20000000000
χ2322222-2-222-2-22-2-2-222222-2-22-20000000000000000-2200000000
χ2422222-2-222-2-22-2-2-22222-222-2-200000000000000002-200000000
χ2522222-2-22-2-22-2222-222-20000-2000000002-2200-2000000000000
χ2622222-2-22-2-22-2222-222-20000-200000000-22-2002000000000000
χ2722222-2-22-2-22-22-2-22-2-220000200000000000220-2-20000000000
χ2822222-2-22-2-22-22-2-22-2-220000200000000000-2-20220000000000
χ292222-222-22-2-2-2200000022-2-2022−2−222−2−200000000002−22−20000
χ302222-222-22-2-2-2200000022-2-20−2−222−2−2220000000000−22−220000
χ312222-222-22-2-2-22000000-2-222022−2−222−2−20000000000−22−220000
χ322222-222-22-2-2-22000000-2-2220−2−222−2−22200000000002−22−20000
χ332222-2-2-2-2222-2-20000002-22-20i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i20000
χ342222-2-2-2-2222-2-20000002-22-20−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i20000
χ352222-2-2-2-2222-2-2000000-22-220i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i20000
χ362222-2-2-2-2222-2-2000000-22-220−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i20000
χ374444-444-4-4-444-40000000000000000000000000000000000000
χ384444-4-4-4-4-44-4440000000000000000000000000000000000000
χ394-4-44400-4000000004i−4i0000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000
χ404-4-44400-4000000004i−4i000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000
χ414-4-44400-400000000−4i4i0000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000
χ424-4-44400-400000000−4i4i000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000
χ434-4-44-40040000000400-4000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ444-4-44-40040000000400-400000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ454-4-44-40040000000-4004000002-2-22-222-2000000000000000000
χ464-4-44-40040000000-400400000-222-22-2-22000000000000000000
χ4788-8-800000000042−4200000000000000000000000000000000000
χ4888-8-8000000000−424200000000000000000000000000000000000
χ498-88-808i−8i0000000000000000000000000000000000000000000
χ508-88-80−8i8i0000000000000000000000000000000000000000000

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