Finite Group Databasebeta

← Group #178917

Character table — Group #178917

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size11111111444444448888888161616161616161616161616161616161616161616163232
order12222222224444442244444222444444488888888888824
χ111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-11-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111-1-1111-1-1-11-11-111-1-1-11111-1-1-1-1-1-1-1-111
χ61111111111111111-1-1111-1-1-11-11-111-1-1-1-1-1-1-111111111-1-1
χ71111111111111111-1-1111-1-1-1-11-1-1-1-11111111-1-1-1-11111-1-1
χ81111111111111111-1-1111-1-1-1-11-1-1-1-1111-1-1-1-11111-1-1-1-111
χ911111111-1-111111111-1-1-1-1-1-11111-1-1-1-1111-1-111-1-111-1-11-1
χ1011111111-1-111111111-1-1-1-1-1-11111-1-1-1-11-1-111-1-111-1-111-11
χ1111111111-1-111111111-1-1-1-1-1-1-1-1-111111-111-1-111-1-1-1-111-11
χ1211111111-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-111-1-11111-1-11-1
χ1311111111-1-1111111-1-1-1-1-11111-11-1-1-111-111-1-1-1-111-1-1111-1
χ1411111111-1-1111111-1-1-1-1-11111-11-1-1-111-1-1-11111-1-111-1-1-11
χ1511111111-1-1111111-1-1-1-1-1111-11-1-111-1-1111-1-1-1-11111-1-1-11
χ1611111111-1-1111111-1-1-1-1-1111-11-1-111-1-11-1-11111-1-1-1-1111-1
χ1722222222222-2-2-22-2222-2-2-2-22000-20000000000000000000
χ1822222222222-2-2-22-2-2-22-2-222-200020000000000000000000
χ192222222222-22-2-2-2200-22-20000200002-2-200000000000000
χ202222222222-22-2-2-2200-22-20000-20000-22200000000000000
χ212222222222-2-222-2-200-2-2200020-202-200000000000000000
χ222222222222-2-222-2-200-2-22000-2020-2200000000000000000
χ2322222222-2-22-2-2-22-222-22222-2000-20000000000000000000
χ2422222222-2-22-2-2-22-2-2-2-222-2-2200020000000000000000000
χ2522222222-2-2-22-2-2-22002-22000020000-22-200000000000000
χ2622222222-2-2-22-2-2-22002-220000-200002-2200000000000000
χ2722222222-2-2-2-222-2-20022-200020-20-2200000000000000000
χ2822222222-2-2-2-222-2-20022-2000-20202-200000000000000000
χ29444-4-4-4-44004000-40000004i−4i000000000000000000000000
χ30444-4-4-4-44004000-4000000−4i4i000000000000000000000000
χ31444-4-4-4-4400-4000404-400000000000000000000000000000
χ32444-4-4-4-4400-400040-4400000000000000000000000000000
χ3344-444-4-4-40004000-400000000000000000002i2−2i20000000000
χ3444-444-4-4-40004000-40000000000000000000−2i22i20000000000
χ3544-444-4-4-4000-400040000000000000000022−22000000000000
χ3644-444-4-4-4000-4000400000000000000000−2222000000000000
χ374-4-44-44-4400004-400000000000000000000000000022−220000
χ384-4-44-44-4400004-4000000000000000000000000000−22220000
χ394-4-44-44-440000-440000000000000000000000000000022−2200
χ404-4-44-44-440000-4400000000000000000000000000000−222200
χ414-4-4-44-4444-40000000000000000000000000002-22-2000000
χ424-4-4-44-4444-4000000000000000000000000000-22-22000000
χ434-4-4-44-444-440000000000000000000000000002-2-22000000
χ444-4-4-44-444-44000000000000000000000000000-222-2000000
χ4588-8-8-888-8000000000000000000000000000000000000000
χ468-888-8-88-8000000000000000000000000000000000000000
χ478-88-888-8-8000000000000000000000000000000000000000

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