Finite Group Databasebeta

← Group #98302

Character table — Group #98302

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222224444444444222244444222444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1111-1-1-1-1-111-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1111-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111-1-1111-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1111-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111
χ711111111111111111111-1-1-1-11-1-1-1-1-111-1-111-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-11-1-1-1-1-111-1-111-1-1-1-1-111111111-1-1-1-1
χ911111111-1-1-11111-1-1-1-1-111111-1-111-111-11-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-11111-1-1-1-1-111111-1-111-111-11-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-11111-1-1-1-1-111-1-11-1-1-1-11-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ1211111111-1-1-11111-1-1-1-1-111-1-11-1-1-1-11-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ1311111111-1-1-11111-1-1-1-1-1-1-11111111-1-1-11-111-1ii−i−iii−i−i−i−iii−i−iii
χ1411111111-1-1-11111-1-1-1-1-1-1-11111111-1-1-11-111-1−i−iii−i−iiiii−i−iii−i−i
χ1511111111-1-1-11111-1-1-1-1-1-1-1-1-1111-1-11111-1-1-11ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-11111-1-1-1-1-1-1-1-1-1111-1-11111-1-1-11−i−iiiii−i−iii−i−i−i−iii
χ1722222222222-2-2-2-2-2-2-22-200002000002-2002-200000000000000000
χ1822222222222-2-2-2-2-2-2-22-20000200000-2200-2200000000000000000
χ192222222222-222-2-2-222-2-20022-200-2-2-200000020000000000000000
χ202222222222-222-2-2-222-2-200-2-2-200222000000-20000000000000000
χ212222222222-2-2-2222-2-2-222200-22200000-2-20000000000000000000
χ222222222222-2-2-2222-2-2-22-2-200-2-2-200000220000000000000000000
χ2322222222-2-2222-2-22-2-2220022-200-2-22000000-20000000000000000
χ2422222222-2-2222-2-22-2-22200-2-2-20022-200000020000000000000000
χ2522222222-2-22-2-222-2222-22200-2-2-2000002-20000000000000000000
χ2622222222-2-22-2-222-2222-2-2-200-22200000-220000000000000000000
χ2722222222-2-2-2-2-2-2-2222-2200002000002-200-2200000000000000000
χ2822222222-2-2-2-2-2-2-2222-220000200000-22002-200000000000000000
χ292-22-2-22-222-20002-22000-22-20002-200000000000000i2−i2i2−i20000i2−i2i2−i2
χ302-22-2-22-222-20002-22000-22-20002-200000000000000−i2i2−i2i20000−i2i2−i2i2
χ312-22-2-22-222-20002-22000-2-22000-2200000000000000i2−i2i2−i20000−i2i2−i2i2
χ322-22-2-22-222-20002-22000-2-22000-2200000000000000−i2i2−i2i20000i2−i2i2−i2
χ332-22-2-22-22-220002-2-200022-2000-22000000000000002−2−2200002−2−22
χ342-22-2-22-22-220002-2-200022-2000-2200000000000000−222−20000−222−2
χ352-22-2-22-22-220002-2-20002-220002-2000000000000002−2−220000−222−2
χ362-22-2-22-22-220002-2-20002-220002-200000000000000−222−200002−2−22
χ374444-4-4-4-4000000004i−4i0000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ384444-4-4-4-4000000004i−4i000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ394444-4-4-4-400000000−4i4i0000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ404444-4-4-4-400000000−4i4i000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ414-44-4-44-444-4000-44-40004000000000000000000000000000000000
χ424-44-4-44-44-44000-444000-4000000000000000000000000000000000
χ434-4-4444-4-40040000000-40000000000000000002i−2i2i−2i000000000000
χ444-4-4444-4-40040000000-4000000000000000000−2i2i−2i2i000000000000
χ454-4-4444-4-400-4000000040000000000000000002-2-22000000000000
χ464-4-4444-4-400-400000004000000000000000000-222-2000000000000
χ474-4-44-4-4440004-4000000000000004-4000000000000000000000000
χ484-4-44-4-4440004-400000000000000-44000000000000000000000000
χ494-4-44-4-444000-440000000004-400000000000000000000000000000
χ504-4-44-4-444000-44000000000-4400000000000000000000000000000
χ5188-8-88-8-88000000000000000000000000000000000000000000000
χ5288-8-8-888-8000000000000000000000000000000000000000000000
χ538-88-88-88-8000000000000000000000000000000000000000000000

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