Finite Group Databasebeta

← Group #176848

Character table — Group #176848

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111111114444444444888888888816161616161616161616161616161616161616163232
order12222222444444444444444444442224444488888888888844
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-11-1-11-1-1-11-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111-1-11-1-11-1-1-11-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111-1-1-1-111111-11-1-1-11-1-11111-1-1-1-11111-1-1
χ61111111111111111111-1-1-1-111111-11-1-1-11-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111-1-1-1-1-1-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-111111111-1-1
χ91111111111-1-1-1-11111-111-1-111-1-1-1-1-1-1-1111111-1-111-1-111-1-11-1
χ101111111111-1-1-1-11111-111-1-111-1-1-1-1-1-1-11111-1-111-1-111-1-111-11
χ111111111111-1-1-1-11111-111-1-1-1-1-111-11111-1-1-111-1-111-1-1-1-111-11
χ121111111111-1-1-1-11111-111-1-1-1-1-111-11111-1-1-1-1-111-1-11111-1-11-1
χ131111111111-1-1-1-11111-1-1-11111-1-1-11-111-11-1-111-1-1-1-11111-1-1-11
χ141111111111-1-1-1-11111-1-1-11111-1-1-11-111-11-1-1-1-11111-1-1-1-1111-1
χ151111111111-1-1-1-11111-1-1-111-1-1-11111-1-1-1-11111-1-1-1-111-1-1111-1
χ161111111111-1-1-1-11111-1-1-111-1-1-11111-1-1-1-111-1-11111-1-111-1-1-11
χ17222222222-222-2-2-2-22-22000022-2-2-202000-20000000000000000
χ18222222222-222-2-2-2-22-220000-2-2-2220-200020000000000000000
χ19222222222-2-2-222-2-22-2-20000222220-2000-20000000000000000
χ20222222222-2-2-222-2-22-2-20000-2-22-2-20200020000000000000000
χ2122222222-222222-2-2-22-2222200-200-2000-200000000000000000
χ2222222222-222222-2-2-22-2-2-2-2-200-2002000200000000000000000
χ2322222222-22-2-2-2-2-2-2-22222-2-2002002000-200000000000000000
χ2422222222-22-2-2-2-2-2-2-222-2-22200200-2000200000000000000000
χ2522222222-2-222-2-222-2-2-2000000200002-2002-200000000000000
χ2622222222-2-222-2-222-2-2-200000020000-2200-2200000000000000
χ2722222222-2-2-2-22222-2-22000000-200002-200-2200000000000000
χ2822222222-2-2-2-22222-2-22000000-20000-22002-200000000000000
χ29444-44-4-4-440000000-40000004-40000000000000000000000000
χ30444-44-4-4-440000000-4000000-440000000000000000000000000
χ31444-44-4-4-4-4000000040000000004i−4i0000000000000000000000
χ32444-44-4-4-4-400000004000000000−4i4i0000000000000000000000
χ334-444-4-4-44040000000-40004i−4i000000000000000000000000000
χ344-444-4-4-44040000000-4000−4i4i000000000000000000000000000
χ354-444-4-4-440-40000000404-400000000000000000000000000000
χ364-444-4-4-440-4000000040-4400000000000000000000000000000
χ374-44-4-444-400004-400000000000000000000002i−2i2i−2i0000000000
χ384-44-4-444-400004-40000000000000000000000−2i2i−2i2i0000000000
χ394-44-4-444-40000-4400000000000000000000002i−2i−2i2i0000000000
χ404-44-4-444-40000-440000000000000000000000−2i2i2i−2i0000000000
χ414-4-4444-4-4004-4000000000000000000000000000000002i−2i2i−2i00
χ424-4-4444-4-4004-400000000000000000000000000000000−2i2i−2i2i00
χ434-4-4444-4-400-44000000000000000000000000000000002i−2i−2i2i00
χ444-4-4444-4-400-4400000000000000000000000000000000−2i2i2i−2i00
χ454-4-4-44-4440000004-40000000000000000000000000022−22000000
χ464-4-4-44-4440000004-400000000000000000000000000−2222000000
χ474-4-4-44-444000000-4400000000000000000000000022−2200000000
χ484-4-4-44-444000000-44000000000000000000000000−222200000000
χ4988-88-8-88-8000000000000000000000000000000000000000000
χ5088-8-8-88-88000000000000000000000000000000000000000000

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