Finite Group Databasebeta

← Group #176705

Character table — Group #176705

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111111114444444444888888888816161616161616161616161616161616161616163232
order12222222444444444444444444442444444488888888888844
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-11-1-1-1-1-11-1-11-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111-1-11-1-1-1-1-11-1-11-1-1-1-1-111111111-1-1
χ51111111111111111111-1-1-1-111111-11-1-11-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111-1-1-1-111111-11-1-11-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111-1-1-1-1-1-11-1-11-11-1-11-111111-1-1-1-11111-1-1
χ81111111111111111111-1-1-1-1-1-11-1-11-11-1-11-11-1-1-1-11111-1-1-1-111
χ9111111111-1-11-1-11111-111-1-111-1-1-11-1-111-1-1111-1-111-1-111-1-11-1
χ10111111111-1-11-1-11111-111-1-111-1-1-11-1-111-1-11-1-111-1-111-1-111-11
χ11111111111-1-11-1-11111-111-1-1-1-1-111-1111-11-1-111-1-1-1-111-1-1111-1
χ12111111111-1-11-1-11111-111-1-1-1-1-111-1111-11-1-1-1-11111-1-111-1-1-11
χ13111111111-1-11-1-11111-1-1-11111-1-1-1-1-11-1111-111-1-111-1-1-1-111-11
χ14111111111-1-11-1-11111-1-1-11111-1-1-1-1-11-1111-1-1-111-1-11111-1-11-1
χ15111111111-1-11-1-11111-1-1-111-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-11
χ16111111111-1-11-1-11111-1-1-111-1-1-11111-1-1-1-111-1-11111-1-1-1-1111-1
χ1722222222222-2-2-2-2-22-2-200000020020-20020-200000000000000
χ1822222222222-2-2-2-2-22-2-2000000200-20200-20200000000000000
χ19222222222-2-2-222-2-22-22000000-20020200-20-200000000000000
χ20222222222-2-2-222-2-22-22000000-200-20-20020200000000000000
χ2122222222-2222-2-2-2-2-222000022-2220-200-200000000000000000
χ2222222222-2222-2-2-2-2-2220000-2-2-2-2-20200200000000000000000
χ2322222222-222-22222-2-2-2222200-200000-200-2000000000000000
χ2422222222-222-22222-2-2-2-2-2-2-200-2000002002000000000000000
χ2522222222-2-2-2222-2-2-22-20000222-2-20200-200000000000000000
χ2622222222-2-2-2222-2-2-22-20000-2-22220-200200000000000000000
χ2722222222-2-2-2-2-2-222-2-2222-2-200200000-2002000000000000000
χ2822222222-2-2-2-2-2-222-2-22-2-22200200000200-2000000000000000
χ29444-4-4-44-440000000-40000000000000000000000000000022−2200
χ30444-4-4-44-440000000-400000000000000000000000000000−222200
χ31444-4-4-44-4-4000000040000000000000000000000000002i2−2i20000
χ32444-4-4-44-4-400000004000000000000000000000000000−2i22i20000
χ3344-44-4-4-4404i−4i000000000000000000000000000002i−2i2-2000000
χ3444-44-4-4-4404i−4i00000000000000000000000000000−2i2i-22000000
χ3544-44-4-4-440−4i4i000000000000000000000000000002i−2i-22000000
χ3644-44-4-4-440−4i4i00000000000000000000000000000−2i2i2-2000000
χ374-44-44-4-440000004-4000004i−4i000000000000000000000000000
χ384-44-44-4-440000004-400000−4i4i000000000000000000000000000
χ394-44-44-4-44000000-440004i−4i00000000000000000000000000000
χ404-44-44-4-44000000-44000−4i4i00000000000000000000000000000
χ414-4-444-44-400004i−4i00000000000000000000002-22i−2i0000000000
χ424-4-444-44-400004i−4i0000000000000000000000-22−2i2i0000000000
χ434-4-444-44-40000−4i4i00000000000000000000002-2−2i2i0000000000
χ444-4-444-44-40000−4i4i0000000000000000000000-222i−2i0000000000
χ454-4-4-4-4444000400000-4000004i−4i0000000000000000000000000
χ464-4-4-4-4444000400000-400000−4i4i0000000000000000000000000
χ474-4-4-4-4444000-4000004000000004-40000000000000000000000
χ484-4-4-4-4444000-400000400000000-440000000000000000000000
χ4988-8-888-8-8000000000000000000000000000000000000000000
χ508-888-88-8-8000000000000000000000000000000000000000000

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