Finite Group Databasebeta

← Group #98393

Character table — Group #98393

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444444444444224444448888888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111-1-1-1-11111-11-11-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111-1-1-1-11111-11-11-1-1-1-1-1-1-1-11111-1-1-1-11111
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
χ911111111-111-1-111-1-1-1-1-11111111-1-1-11-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-111-1-111-1-1-1-1-11111111-1-1-11-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-111-1-111-1-1-1-1-111111-1-111-1-1-11-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-111-1-111-1-1-1-1-111111-1-111-1-1-11-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-111-1-111-1-1-1-1-11-1-1-1-111-1-1111-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-111-1-111-1-1-1-1-11-1-1-1-111-1-1111-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-111-1-111-1-1-1-1-11-1-1-1-1-1-1111-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-111-1-111-1-1-1-1-11-1-1-1-1-1-1111-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-222-2-2-222-2-2000020-2000000000000000000000
χ18222222222222-2-2-2-222-2-2-2-2-2220000-202000000000000000000000
χ19222222222-2-2-22-2-2-22-22-220000000000002-22-20000000000000000
χ20222222222-2-2-22-2-2-22-22-22000000000000-22-220000000000000000
χ21222222222-2-2-2-22222-2-22-2000022-2-20-20200000000000000000000
χ22222222222-2-2-2-22222-2-22-20000-2-222020-200000000000000000000
χ2322222222-222-22-2-22-2-222-222-2-20000-202000000000000000000000
χ2422222222-222-22-2-22-2-222-2-2-222000020-2000000000000000000000
χ2522222222-2-2-22222-2-222-2-2000022220-20-200000000000000000000
χ2622222222-2-2-22222-2-222-2-20000-2-2-2-2020200000000000000000000
χ2722222222-2-2-22-2-2-22-22-2220000000000002-2-220000000000000000
χ2822222222-2-2-22-2-2-22-22-222000000000000-222-20000000000000000
χ292-222-2-22-20002-22-200-220000002i−2i2i−2i00000000i2−i2i2−i200002−22−20000
χ302-222-2-22-20002-22-200-220000002i−2i2i−2i00000000−i2i2−i2i20000−22−220000
χ312-222-2-22-20002-22-200-22000000−2i2i−2i2i00000000i2−i2i2−i20000−22−220000
χ322-222-2-22-20002-22-200-22000000−2i2i−2i2i00000000−i2i2−i2i200002−22−20000
χ332-222-2-22-2000-222-2002-20000002i−2i−2i2i000000002−2−220000−i2i2i2−i20000
χ342-222-2-22-2000-222-2002-20000002i−2i−2i2i00000000−222−20000i2−i2−i2i20000
χ352-222-2-22-2000-222-2002-2000000−2i2i2i−2i000000002−2−220000i2−i2−i2i20000
χ362-222-2-22-2000-222-2002-2000000−2i2i2i−2i00000000−222−20000−i2i2i2−i20000
χ37444-44-4-4-440000000-4000000000000000000000000000000002-22-2
χ38444-44-4-4-440000000-400000000000000000000000000000000-22-22
χ39444-44-4-4-4-400000004000000000000000000000000000000002i−2i−2i2i
χ40444-44-4-4-4-40000000400000000000000000000000000000000−2i2i2i−2i
χ414-444-4-44-400044-4400-4-40000000000000000000000000000000000
χ424-444-4-44-4000-4-4-4400440000000000000000000000000000000000
χ434-4-444-4-4400000004000-40000000000000000000002i−2i2i−2i00000000
χ444-4-444-4-4400000004000-4000000000000000000000−2i2i−2i2i00000000
χ454-4-444-4-440000000-400040000000000000000000002-2-2200000000
χ464-4-444-4-440000000-40004000000000000000000000-222-200000000
χ474-4-4-4444-404-40000000000004i−4i0000000000000000000000000000
χ484-4-4-4444-404-4000000000000−4i4i0000000000000000000000000000
χ494-4-4-4444-40-4400000000004i−4i000000000000000000000000000000
χ504-4-4-4444-40-440000000000−4i4i000000000000000000000000000000
χ5188-88-88-8-8000000000000000000000000000000000000000000000
χ5288-8-8-8-888000000000000000000000000000000000000000000000
χ538-88-8-88-88000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).