Finite Group Databasebeta

← Group #98305

Character table — Group #98305

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222224444444444444444444224444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111-1-111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ911111111-1-11111-1-1-1-1-1-111111-1-111-1-1-11-1-111ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-11111-1-1-1-1-1-111111-1-111-1-1-11-1-111−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-11111-1-1-1-1-1-1111-1-1-1-1-1-111-1111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1211111111-1-11111-1-1-1-1-1-1111-1-1-1-1-1-111-1111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1311111111-1-11111-1-1-1-1-1-11-1-1111111111-1-1-1-1-1ii−i−iii−i−i−i−iii−i−iii
χ1411111111-1-11111-1-1-1-1-1-11-1-1111111111-1-1-1-1-1−i−iii−i−iiiii−i−iii−i−i
χ1511111111-1-11111-1-1-1-1-1-11-1-1-1-111-1-1-1-11-11111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-11111-1-1-1-1-1-11-1-1-1-111-1-1-1-11-11111−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-222-2-2-2002200-2-20000-22000000000000000000
χ18222222222222-2-2-2-222-2-2-200-2-2002200002-2000000000000000000
χ192222222222-2-2222-2-2-22-2-22200220000-2-200000000000000000000
χ202222222222-2-2222-2-2-22-2-2-2-200-2-200002200000000000000000000
χ212222222222-2-2-2-2-22-2-2-222000000002-200002-20000000000000000
χ222222222222-2-2-2-2-22-2-2-22200000000-220000-220000000000000000
χ2322222222-2-222-2-222-2-222-2002200-2-200002-2000000000000000000
χ2422222222-2-222-2-222-2-222-200-2-200220000-22000000000000000000
χ2522222222-2-2-2-222-2222-22-22200-2-200002-200000000000000000000
χ2622222222-2-2-2-222-2222-22-2-2-200220000-2200000000000000000000
χ2722222222-2-2-2-2-2-22-2222-22000000002-20000-220000000000000000
χ2822222222-2-2-2-2-2-22-2222-2200000000-2200002-20000000000000000
χ292-2-2-222-222-2002-22000-2002-2002-200000000000000i2−i2i2−i20000i2−i2i2−i2
χ302-2-2-222-222-2002-22000-2002-2002-200000000000000−i2i2−i2i20000−i2i2−i2i2
χ312-2-2-222-222-2002-22000-200-2200-2200000000000000i2−i2i2−i20000−i2i2−i2i2
χ322-2-2-222-222-2002-22000-200-2200-2200000000000000−i2i2−i2i20000i2−i2i2−i2
χ332-2-2-222-22-22002-2-20002002-200-22000000000000002−2−2200002−2−22
χ342-2-2-222-22-22002-2-20002002-200-2200000000000000−222−20000−222−2
χ352-2-2-222-22-22002-2-2000200-22002-2000000000000002−2−220000−222−2
χ362-2-2-222-22-22002-2-2000200-22002-200000000000000−222−200002−2−22
χ3744-4-4-4-44400000004000-4000000000000000002i−2i2i−2i000000000000
χ3844-4-4-4-44400000004000-400000000000000000−2i2i−2i2i000000000000
χ3944-4-4-4-4440000000-40004000000000000000002-2-22000000000000
χ4044-4-4-4-4440000000-4000400000000000000000-222-2000000000000
χ414-44-44-44-4000000004i−4i0000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ424-44-44-44-4000000004i−4i000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ434-44-44-44-400000000−4i4i0000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ444-44-44-44-400000000−4i4i000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ454-4-44-444-4004-40000000000000004i−4i000000000000000000000000
χ464-4-44-444-4004-4000000000000000−4i4i000000000000000000000000
χ474-4-44-444-400-44000000000004i−4i0000000000000000000000000000
χ484-4-44-444-400-4400000000000−4i4i0000000000000000000000000000
χ494-4-4-444-444-400-44-400040000000000000000000000000000000000
χ504-4-4-444-44-4400-444000-40000000000000000000000000000000000
χ51888-8-88-8-8000000000000000000000000000000000000000000000
χ5288-888-8-8-8000000000000000000000000000000000000000000000
χ538-888-8-8-88000000000000000000000000000000000000000000000

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