Finite Group Databasebeta

← Group #175238

Character table — Group #175238

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222224444444444224444444244444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-111-1-11-11-1-11-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-111-1-11-11-1-11-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111-1-111-1-1111-1-1-1-1-11-111111-1-1-1-1-1-1-1-11111
χ611111111111111111111-1-111-1-1111-1-1-1-1-11-11-1-1-1-111111111-1-1-1-1
χ711111111111111111111-1-1-1-1-1-1-1-111-111-1-11-111111111-1-1-1-1-1-1-1-1
χ811111111111111111111-1-1-1-1-1-1-1-111-111-1-11-1-1-1-1-1-1-1-1-111111111
χ911111111-1-1-1-11-1-1111111111-1-1-1-1-1111-1-11-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11-1-1111111111-1-1-1-1-1111-1-11-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-11-1-11111111-1-1-1-111-1-11-11-1-11111-1-1-1-11111-1-1-1-111
χ1211111111-1-1-1-11-1-11111111-1-1-1-111-1-11-11-1-111-1-11111-1-1-1-11111-1-1
χ1311111111-1-1-1-11-1-111111-1-11111-1-1-1-1-1-11111-111-1-1-1-111-1-11111-1-1
χ1411111111-1-1-1-11-1-111111-1-11111-1-1-1-1-1-11111-1-1-11111-1-111-1-1-1-111
χ1511111111-1-1-1-11-1-111111-1-1-1-11111-11-11-11-1-1111-1-111-1-1-1-111-1-111
χ1611111111-1-1-1-11-1-111111-1-1-1-11111-11-11-11-1-11-1-111-1-11111-1-111-1-1
χ17222222222222-2-2-2-222-2-200000000-220-2-200200000000000000000
χ18222222222222-2-2-2-222-2-200000000-2-202200-200000000000000000
χ192222222222-2-2222-2-2-22-22200-2-200-20-20020000000000000000000
χ202222222222-2-2222-2-2-22-2-2-2002200-20200-20000000000000000000
χ212222222222-2-2-2-2-22-2-2-22002200-2-2200000-2020000000000000000
χ222222222222-2-2-2-2-22-2-2-2200-2-2002220000020-20000000000000000
χ2322222222-2-2222-2-2-2-2-22-22200220020-200-20000000000000000000
χ2422222222-2-2222-2-2-2-2-22-2-2-200-2-2002020020000000000000000000
χ2522222222-2-222-2222-2-2-2200220022-200000-20-20000000000000000
χ2622222222-2-222-2222-2-2-2200-2-200-2-2-2000002020000000000000000
χ2722222222-2-2-2-2-222-222-2-200000000220-2200-200000000000000000
χ2822222222-2-2-2-2-222-222-2-2000000002-202-200200000000000000000
χ294444-4-4-4-4000000004-4000000000000000000000000000000022−2200
χ304444-4-4-4-4000000004-40000000000000000000000000000000−222200
χ314444-4-4-4-400000000-4400000000000000000000000000000000022−22
χ324444-4-4-4-400000000-44000000000000000000000000000000000−2222
χ3344-4-444-4-40000400000-404-40000000000000000000000000000000
χ3444-4-444-4-40000400000-40-440000000000000000000000000000000
χ3544-4-444-4-40000-4000004000004i−4i000000000000000000000000000
χ3644-4-444-4-40000-400000400000−4i4i000000000000000000000000000
χ374-44-44-4-4400000004000-40000004i−4i0000000000000000000000000
χ384-44-44-4-4400000004000-4000000−4i4i0000000000000000000000000
χ394-44-44-4-440000000-40004004-400000000000000000000000000000
χ404-44-44-4-440000000-4000400-4400000000000000000000000000000
χ414-44-4-444-44-4000000000000000000000000000000000002i−2i2i−2i0000
χ424-44-4-444-44-400000000000000000000000000000000000−2i2i−2i2i0000
χ434-44-4-444-4-44000000000000000000000000000000000002i−2i−2i2i0000
χ444-44-4-444-4-4400000000000000000000000000000000000−2i2i2i−2i0000
χ454-4-444-44-4004-4000000000000000000000000000002i−2i2i−2i00000000
χ464-4-444-44-4004-400000000000000000000000000000−2i2i−2i2i00000000
χ474-4-444-44-400-44000000000000000000000000000002i−2i−2i2i00000000
χ484-4-444-44-400-4400000000000000000000000000000−2i2i2i−2i00000000
χ494-4-44-44-44000004-400000000000000000000002-22-2000000000000
χ504-4-44-44-44000004-40000000000000000000000-22-22000000000000
χ514-4-44-44-4400000-4400000000000000000000002-2-22000000000000
χ524-4-44-44-4400000-440000000000000000000000-222-2000000000000
χ5388-8-8-8-888000000000000000000000000000000000000000000000

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