Finite Group Databasebeta

← Group #175010

Character table — Group #175010

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444444444444244444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111-1-1-1-111111-1-1-11-1-1-11111-1-1-1-1-1-1-1-11111
χ6111111111111111111111-1-1-1-111111-1-1-11-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111-1-1-1-1-1-1-1-1-11-1-1-11111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-11111-1-1-1-11111
χ911111111-1-11-1-1-1-111111-111-1-111-1-1-111-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-11-1-1-1-111111-111-1-111-1-1-111-111-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-11-1-1-1-111111-111-1-1-1-1111-11-1-1-11111-1-111-1-1-1-111-1-111
χ1211111111-1-11-1-1-1-111111-111-1-1-1-1111-11-1-1-111-1-111-1-11111-1-111-1-1
χ1311111111-1-11-1-1-1-111111-1-1-11111-1-1-1-1-111-11111-1-1-1-111-1-11111-1-1
χ1411111111-1-11-1-1-1-111111-1-1-11111-1-1-1-1-111-111-1-11111-1-111-1-1-1-111
χ1511111111-1-11-1-1-1-111111-1-1-111-1-11111-11-11-1-111-1-1-1-11111-1-1-1-111
χ1611111111-1-11-1-1-1-111111-1-1-111-1-11111-11-11-1-1-1-11111-1-1-1-11111-1-1
χ172222222222222-2-2-2-2-2-22-2000022-2-22000-20000000000000000000
χ182222222222222-2-2-2-2-2-22-20000-2-222-200020000000000000000000
χ192222222222-2-2-222-2-222-2-20000000002000-22-20000000000000000
χ202222222222-2-2-222-2-222-2-2000000000-20002-220000000000000000
χ212222222222-2-2-2-2-222-2-2-2222-2-2000000-2200000000000000000000
χ222222222222-2-2-2-2-222-2-2-22-2-2220000002-200000000000000000000
χ2322222222-2-22-2-222-2-2-2-22200002222-2000-20000000000000000000
χ2422222222-2-22-2-222-2-2-2-2220000-2-2-2-2200020000000000000000000
χ2522222222-2-2-2222222-2-2-2-22222000000-2-200000000000000000000
χ2622222222-2-2-2222222-2-2-2-2-2-2-2-20000002200000000000000000000
χ2722222222-2-2-222-2-2-2-222-220000000002000-2-220000000000000000
χ2822222222-2-2-222-2-2-2-222-22000000000-200022-20000000000000000
χ294444-4-4-4-400400000000-4000004-400000000000000000000000000
χ304444-4-4-4-400400000000-400000-4400000000000000000000000000
χ314444-4-4-4-400-400000000400000004i−4i000000000000000000000000
χ324444-4-4-4-400-40000000040000000−4i4i000000000000000000000000
χ3344-4-4-4-4440000000004-40000000000000000000000002i2−2i200000000
χ3444-4-4-4-4440000000004-4000000000000000000000000−2i22i200000000
χ3544-4-4-4-444000000000-4400000000000000000000002i2−2i20000000000
χ3644-4-4-4-444000000000-440000000000000000000000−2i22i20000000000
χ374-44-44-44-40004i−4i0000000000000000000000002-22i−2i000000000000
χ384-44-44-44-40004i−4i000000000000000000000000-22−2i2i000000000000
χ394-44-44-44-4000−4i4i0000000000000000000000002-2−2i2i000000000000
χ404-44-44-44-4000−4i4i000000000000000000000000-222i−2i000000000000
χ414-44-4-44-444i−4i0000000000000000000000000000000000000002-22i−2i
χ424-44-4-44-444i−4i000000000000000000000000000000000000000-22−2i2i
χ434-44-4-44-44−4i4i0000000000000000000000000000000000000002-2−2i2i
χ444-44-4-44-44−4i4i000000000000000000000000000000000000000-222i−2i
χ454-4-444-4-4400000004-40000004i−4i0000000000000000000000000000
χ464-4-444-4-4400000004-4000000−4i4i0000000000000000000000000000
χ474-4-444-4-440000000-4400004i−4i000000000000000000000000000000
χ484-4-444-4-440000000-440000−4i4i000000000000000000000000000000
χ494-4-44-444-4000004i−4i0000000000000000000000000000002i−2i2-20000
χ504-4-44-444-4000004i−4i000000000000000000000000000000−2i2i-220000
χ514-4-44-444-400000−4i4i0000000000000000000000000000002i−2i-220000
χ524-4-44-444-400000−4i4i000000000000000000000000000000−2i2i2-20000
χ5388-8-888-8-8000000000000000000000000000000000000000000000

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