Finite Group Databasebeta

← Group #176290

Character table — Group #176290

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111122224444448888888888888881616161616161616161616161616161616163232
order12222222444444444424444444444444444444488888888888824
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111-1-1-1-1111111-1-1-1-1-1-1-111-111111111-1-1-1-1-1-1
χ61111111111111111111-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111-1-1-1-1-1-111-1-111111-1-1-1-111111-1-1-1-11111-1-1
χ81111111111111111111-1-1-1-1-1-111-1-111111-1-1-1-11-1-1-1-11111-1-1-1-111
χ911111111-1-1-1-1111111-111-1-111-1-1-1-111-1-111-11-1-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-1111111-111-1-111-1-1-1-111-1-111-11-1-1-1-111-1-111-1-111-11
χ1111111111-1-1-1-1111111-111-1-1-1-1-1-111-1-111-11-1-11111-1-1-1-111-1-1111-1
χ1211111111-1-1-1-1111111-111-1-1-1-1-1-111-1-111-11-1-111-1-11111-1-111-1-1-11
χ1311111111-1-1-1-1111111-1-1-11111-1-1-1-1-1-111-1-111-1111-1-111-1-1-1-111-11
χ1411111111-1-1-1-1111111-1-1-11111-1-1-1-1-1-111-1-111-11-1-111-1-11111-1-11-1
χ1511111111-1-1-1-1111111-1-1-111-1-1-1-11111-1-11-11-11-111-1-1-1-11111-1-1-11
χ1611111111-1-1-1-1111111-1-1-111-1-1-1-11111-1-11-11-11-1-1-11111-1-1-1-1111-1
χ172222222222222-2-2-22-2-20000002-2002222-20000-200000000000000
χ182222222222222-2-2-22-2-20000002-200-2-2-2-220000200000000000000
χ19222222222222-22-2-2-22-2000022-22220000000-2-2000000000000000
χ20222222222222-22-2-2-22-20000-2-2-22-2-2000000022000000000000000
χ21222222222222-2-222-2-22222200-2-20000000-2-200000000000000000
χ22222222222222-2-222-2-22-2-2-2-200-2-200000002200000000000000000
χ2322222222-2-2-2-22-2-2-22-22000000-220022-2-2-20000200000000000000
χ2422222222-2-2-2-22-2-2-22-22000000-2200-2-22220000-200000000000000
χ2522222222-2-2-2-2-22-2-2-2220000222-2-2-20000000-22000000000000000
χ2622222222-2-2-2-2-22-2-2-2220000-2-22-22200000002-2000000000000000
χ2722222222-2-2-2-2-2-222-2-2-222-2-200220000000-2200000000000000000
χ2822222222-2-2-2-2-2-222-2-2-2-2-222002200000002-200000000000000000
χ294444-4-4-4-40000004-4000004-4000000000000000000000000000000
χ304444-4-4-4-40000004-400000-44000000000000000000000000000000
χ314444-4-4-4-4000000-440004-400000000000000000000000000000000
χ324444-4-4-4-4000000-44000-4400000000000000000000000000000000
χ3344-4-444-4-444-4-40000000000000000000000000002i−2i2i−2i0000000000
χ3444-4-444-4-444-4-4000000000000000000000000000−2i2i−2i2i0000000000
χ3544-4-444-4-4-4-4440000000000000000000000000002i−2i−2i2i0000000000
χ3644-4-444-4-4-4-444000000000000000000000000000−2i2i2i−2i0000000000
χ374-44-44-44-44i−4i4i−4i00000000000000000000000000000002-22i−2i000000
χ384-44-44-44-44i−4i4i−4i0000000000000000000000000000000-22−2i2i000000
χ394-44-44-44-4−4i4i−4i4i00000000000000000000000000000002-2−2i2i000000
χ404-44-44-44-4−4i4i−4i4i0000000000000000000000000000000-222i−2i000000
χ414-44-4-44-44000004000-4000004i−4i0000000000000000000000000000
χ424-44-4-44-44000004000-400000−4i4i0000000000000000000000000000
χ434-44-4-44-4400000-400040000000004-4000000000000000000000000
χ444-44-4-44-4400000-40004000000000-44000000000000000000000000
χ454-4-444-4-444i−4i−4i4i000000000000000000000000000000000002-22i−2i00
χ464-4-444-4-444i−4i−4i4i00000000000000000000000000000000000-22−2i2i00
χ474-4-444-4-44−4i4i4i−4i000000000000000000000000000000000002-2−2i2i00
χ484-4-444-4-44−4i4i4i−4i00000000000000000000000000000000000-222i−2i00
χ494-4-44-444-400004000-4000000000000004i−4i00000000000000000000
χ504-4-44-444-400004000-400000000000000−4i4i00000000000000000000
χ514-4-44-444-40000-400040000000000004-40000000000000000000000
χ524-4-44-444-40000-40004000000000000-440000000000000000000000
χ5388-8-8-8-888000000000000000000000000000000000000000000000

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