Finite Group Databasebeta

← Group #98326

Character table — Group #98326

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222224444444444222244444244444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1111-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1111-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111-1-1111-1-1111-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1111-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111-1-1-1-11-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-11-1-1-1-1-1-1-111-111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-11111-1-1-1-1-111111-1-111-1-11-1-1-111ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-11111-1-1-1-1-111111-1-111-1-11-1-1-111−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-11111-1-1-1-1-111-1-11-1-1-1-11-11111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1211111111-1-1-11111-1-1-1-1-111-1-11-1-1-1-11-11111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1311111111-1-1-11111-1-1-1-1-1-1-11111111-11-111-1-1-1ii−i−iii−i−i−i−iii−i−iii
χ1411111111-1-1-11111-1-1-1-1-1-1-11111111-11-111-1-1-1−i−iii−i−iiiii−i−iii−i−i
χ1511111111-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1111−i−iiiii−i−iii−i−i−i−iii
χ1722222222222-2-2-2-2-2-2-22-20000200000002-202-20000000000000000
χ1822222222222-2-2-2-2-2-2-22-2000020000000-220-220000000000000000
χ192222222222-222-2-2-222-2-20022-200-2-2-200002000000000000000000
χ202222222222-222-2-2-222-2-200-2-2-2002220000-2000000000000000000
χ212222222222-2-2-2222-2-2-222200-222000-2-2000000000000000000000
χ222222222222-2-2-2222-2-2-22-2-200-2-2-200022000000000000000000000
χ2322222222-2-2222-2-22-2-2220022-200-2-220000-2000000000000000000
χ2422222222-2-2222-2-22-2-22200-2-2-20022-200002000000000000000000
χ2522222222-2-22-2-222-2222-22200-2-2-20002-2000000000000000000000
χ2622222222-2-22-2-222-2222-2-2-200-222000-22000000000000000000000
χ2722222222-2-2-2-2-2-2-2222-220000200000002-20-220000000000000000
χ2822222222-2-2-2-2-2-2-2222-22000020000000-2202-20000000000000000
χ2922-2-2-2-2222-20002-22000-22-20002-200000000000000i2−i2i2−i20000i2−i2i2−i2
χ3022-2-2-2-2222-20002-22000-22-20002-200000000000000−i2i2−i2i20000−i2i2−i2i2
χ3122-2-2-2-2222-20002-22000-2-22000-2200000000000000i2−i2i2−i20000−i2i2−i2i2
χ3222-2-2-2-2222-20002-22000-2-22000-2200000000000000−i2i2−i2i20000i2−i2i2−i2
χ3322-2-2-2-222-220002-2-200022-2000-22000000000000002−2−2200002−2−22
χ3422-2-2-2-222-220002-2-200022-2000-2200000000000000−222−20000−222−2
χ3522-2-2-2-222-220002-2-20002-220002-2000000000000002−2−220000−222−2
χ3622-2-2-2-222-220002-2-20002-220002-200000000000000−222−200002−2−22
χ3744-444-4-4-40040000000-40000000000000000002-22-2000000000000
χ3844-444-4-4-40040000000-4000000000000000000-22-22000000000000
χ3944-444-4-4-400-4000000040000000000000000002i−2i−2i2i000000000000
χ4044-444-4-4-400-400000004000000000000000000−2i2i2i−2i000000000000
χ4144-4-4-4-4444-4000-44-40004000000000000000000000000000000000
χ4244-4-4-4-444-44000-444000-4000000000000000000000000000000000
χ434-444-4-44-4000000004i−4i0000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ444-444-4-44-4000000004i−4i000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ454-444-4-44-400000000−4i4i0000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ464-444-4-44-400000000−4i4i000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ474-4-44-44-440004-4000000000000004-4000000000000000000000000
χ484-4-44-44-440004-400000000000000-44000000000000000000000000
χ494-4-44-44-44000-440000000004-400000000000000000000000000000
χ504-4-44-44-44000-44000000000-4400000000000000000000000000000
χ51888-8-88-8-8000000000000000000000000000000000000000000000
χ528-88-88-8-88000000000000000000000000000000000000000000000
χ538-8-8-8888-8000000000000000000000000000000000000000000000

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