Finite Group Databasebeta

← Group #98321

Character table — Group #98321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222224444444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-11-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-111-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111-1-111-1-111-11-11-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111-1-111-1-111-11-11-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111-1-111-1-111-1-1-1-11111111-1-1-11-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-111-1-111-1-1-1-11111111-1-1-11-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-111-1-111-1-1-1-1111-1-11111-1-1-11-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-111-1-111-1-1-1-1111-1-11111-1-1-11-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-111-1-111-1-1-1-11-1-111-1-1-1-1111-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-111-1-111-1-1-1-11-1-111-1-1-1-1111-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-111-1-111-1-1-1-11-1-1-1-1-1-1111-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-111-1-111-1-1-1-11-1-1-1-1-1-1111-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222-2-2-2-2-22-2-2002200220-20-200000000000000000000
χ182222222222222-2-2-2-2-22-2-200-2-200-2-2020200000000000000000000
χ192222222222-2-2-22-2-2-2-2-2220000000000002-22-20000000000000000
χ202222222222-2-2-22-2-2-2-2-222000000000000-22-220000000000000000
χ212222222222-2-2-2-22222-2-2-22200-2-200-202000000000000000000000
χ222222222222-2-2-2-22222-2-2-2-2-200220020-2000000000000000000000
χ2322222222-2-222-22-2-222-22-2002200-2-20-20200000000000000000000
χ2422222222-2-222-22-2-222-22-200-2-20022020-200000000000000000000
χ2522222222-2-2-2-22222-2-222-22200-2-20020-2000000000000000000000
χ2622222222-2-2-2-22222-2-222-2-2-2002200-202000000000000000000000
χ2722222222-2-2-2-22-2-2-2222-220000000000002-2-220000000000000000
χ2822222222-2-2-2-22-2-2-2222-22000000000000-222-20000000000000000
χ292-222-22-2-22-22-2-200000200002i−2i002i−2i000000000000i2−i2i2−i200002−22−2
χ302-222-22-2-22-22-2-200000200002i−2i002i−2i000000000000−i2i2−i2i20000−22−22
χ312-222-22-2-22-22-2-20000020000−2i2i00−2i2i000000000000i2−i2i2−i20000−22−22
χ322-222-22-2-22-22-2-20000020000−2i2i00−2i2i000000000000−i2i2−i2i200002−22−2
χ332-222-22-2-2-222-2200000-200002i−2i00−2i2i0000000000002−2−220000−i2i2i2−i2
χ342-222-22-2-2-222-2200000-200002i−2i00−2i2i000000000000−222−20000i2−i2−i2i2
χ352-222-22-2-2-222-2200000-20000−2i2i002i−2i0000000000002−2−220000i2−i2−i2i2
χ362-222-22-2-2-222-2200000-20000−2i2i002i−2i000000000000−222−20000−i2i2i2−i2
χ3744-4-444-4-400000400000-4000000000000000002-22-2000000000000
χ3844-4-444-4-400000400000-400000000000000000-22-22000000000000
χ3944-4-444-4-400000-4000004000000000000000002i−2i−2i2i000000000000
χ4044-4-444-4-400000-400000400000000000000000−2i2i2i−2i000000000000
χ414-444-44-4-44-4-44400000-40000000000000000000000000000000000
χ424-444-44-4-4-44-44-40000040000000000000000000000000000000000
χ434-44-44-44-40000004-40000000004i−4i00000000000000000000000000
χ444-44-44-44-40000004-4000000000−4i4i00000000000000000000000000
χ454-44-44-44-4000000-44000004i−4i000000000000000000000000000000
χ464-44-44-44-4000000-4400000−4i4i000000000000000000000000000000
χ474-4-444-4-44000000004i−4i0000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ484-4-444-4-44000000004i−4i000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ494-4-444-4-4400000000−4i4i0000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ504-4-444-4-4400000000−4i4i000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ51888-8-8-8-88000000000000000000000000000000000000000000000
χ5288-88-8-88-8000000000000000000000000000000000000000000000
χ538-8-8-8-8888000000000000000000000000000000000000000000000

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