Finite Group Databasebeta

← Group #178753

Character table — Group #178753

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size11111111444444448888888161616161616161616161616161616161616161616163232
order12222222444444442224444444444444488888888888824
χ111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-11-11-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111-1-11-1-1111-1-1-11-11-1-11111-1-1-1-11111-1-1
χ611111111111111111-1-11-1-1111-1-1-11-11-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111-1-11-1-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ811111111111111111-1-11-1-11-1-111-1-1-1-111-1-1-1-111111111-1-1
χ911111111-1-1111111-111-1-1-1-1111-11-1-1-11-111-1-111-1-111-1-11-1
χ1011111111-1-1111111-111-1-1-1-1111-11-1-1-11-1-1-111-1-111-1-111-11
χ1111111111-1-1111111-111-1-1-1-1-1-1-1111-11-1111-1-111-1-1-1-111-11
χ1211111111-1-1111111-111-1-1-1-1-1-1-1111-11-11-1-111-1-11111-1-11-1
χ1311111111-1-1111111-1-1-1-111-111-11-1-11-1-1111-1-1-1-11111-1-1-11
χ1411111111-1-1111111-1-1-1-111-111-11-1-11-1-11-1-11111-1-1-1-1111-1
χ1511111111-1-1111111-1-1-1-111-1-1-11-1-11111-111-1-1-1-111-1-1111-1
χ1611111111-1-1111111-1-1-1-111-1-1-11-1-11111-1-1-11111-1-111-1-1-11
χ17222222222222-2-2-2-2-222-2-2-220000-20200000000000000000
χ18222222222222-2-2-2-2-2-2-2-2222000020-200000000000000000
χ192222222222-2-222-2-2-200200-22-200020-20000000000000000
χ202222222222-2-222-2-2-200200-2-22000-2020000000000000000
χ212222222222-2-2-2-222200-200-2002-20000-2200000000000000
χ222222222222-2-2-2-222200-200-200-2200002-200000000000000
χ2322222222-2-222-2-2-2-2222222-20000-20-200000000000000000
χ2422222222-2-222-2-2-2-22-2-22-2-2-2000020200000000000000000
χ2522222222-2-2-2-222-2-2200-20022-2000-2020000000000000000
χ2622222222-2-2-2-222-2-2200-2002-2200020-20000000000000000
χ2722222222-2-2-2-2-2-222-200200200220000-2-200000000000000
χ2822222222-2-2-2-2-2-222-200200200-2-200002200000000000000
χ294444-4-4-4-4004-4000000004-40000000000000000000000000
χ304444-4-4-4-4004-400000000-440000000000000000000000000
χ314444-4-4-4-400-44000004-40000000000000000000000000000
χ324444-4-4-4-400-4400000-440000000000000000000000000000
χ3344-4-44-44-400004-40000000000000000000002i2−2i20000000000
χ3444-4-44-44-400004-4000000000000000000000−2i22i20000000000
χ3544-4-44-44-40000-4400000000000000000002i2−2i2000000000000
χ3644-4-44-44-40000-440000000000000000000−2i22i2000000000000
χ374-44-444-4-44i−4i0000000000000000000000000002-22i−2i000000
χ384-44-444-4-44i−4i000000000000000000000000000-22−2i2i000000
χ394-44-444-4-4−4i4i0000000000000000000000000002-2−2i2i000000
χ404-44-444-4-4−4i4i000000000000000000000000000-222i−2i000000
χ414-44-4-4-4440000004-400000000000000000000000000022−2200
χ424-44-4-4-4440000004-4000000000000000000000000000−222200
χ434-44-4-4-444000000-44000000000000000000000000022−220000
χ444-44-4-4-444000000-440000000000000000000000000−22220000
χ4588-8-8-88-88000000000000000000000000000000000000000
χ468-8-888-8-88000000000000000000000000000000000000000
χ478-8-88-888-8000000000000000000000000000000000000000

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