Finite Group Databasebeta

← Group #175221

Character table — Group #175221

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444222224444222444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111-1-111-1-111-111-1-11-11-1-111-1-1-1-11111-1-1-1-1
χ6111111111111111111111-1-111-1-111-1-1-1-1-11-11-1-1-1-11111-1-1-1-11111
χ7111111111111111111111-1-1-1-1-1-1-1-1111-1-1-11-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-11-111-1-111111111-1-1-1-1
χ9111111111-1-11-1-1-1-11111-11111-1-1-1-11111-1-111-1-1-1-111-1-111-1-111-1-1
χ10111111111-1-11-1-1-1-11111-11111-1-1-1-11-1-11-1-111-1-111-1-111-1-111-1-111
χ11111111111-1-11-1-1-1-11111-111-1-1-1-111-1111-11-1-111-1-111-1-1-1-111-1-111
χ12111111111-1-11-1-1-1-11111-111-1-1-1-111-1-1-11-11-1-11111-1-11111-1-111-1-1
χ13111111111-1-11-1-1-1-11111-1-1-11111-1-1-111-11-1-1111-1-1-1-11111-1-1-1-111
χ14111111111-1-11-1-1-1-11111-1-1-11111-1-1-1-1-1-11-1-11111111-1-1-1-11111-1-1
χ15111111111-1-11-1-1-1-11111-1-1-1-1-11111111-1111-1-1-1-1-1-1-111-1-11111-1-1
χ16111111111-1-11-1-1-1-11111-1-1-1-1-111111-1-1-1111-1-1-11111-1-111-1-1-1-111
χ1722222222222-2-2-2-2-2-2-22-2200000000200000-202-200000000000000
χ1822222222222-2-2-2-2-2-2-22-2200000000-20000020-2200000000000000
χ19222222222-2-2-22222-2-22-2-200000000200000-20-2200000000000000
χ20222222222-2-2-22222-2-22-2-200000000-200000202-200000000000000
χ2122222222-222222-2-2-2-2-22-20022002200000-20-20000000000000000
χ2222222222-222222-2-2-2-2-22-200-2-200-2-2000002020000000000000000
χ2322222222-222-2-2-22222-2-2-22200-2-200000-220000000000000000000
χ2422222222-222-2-2-22222-2-2-2-2-20022000002-20000000000000000000
χ2522222222-2-2-22-2-222-2-2-222002200-2-20000020-20000000000000000
χ2622222222-2-2-22-2-222-2-2-22200-2-2002200000-2020000000000000000
χ2722222222-2-2-2-222-2-222-2-2222002200000-2-20000000000000000000
χ2822222222-2-2-2-222-2-222-2-22-2-200-2-200000220000000000000000000
χ29444-4-44-4-40000004i−4i00000000000000000000000002-22i−2i00000000
χ30444-4-44-4-40000004i−4i0000000000000000000000000-22−2i2i00000000
χ31444-4-44-4-4000000−4i4i00000000000000000000000002-2−2i2i00000000
χ32444-4-44-4-4000000−4i4i0000000000000000000000000-222i−2i00000000
χ3344-444-4-4-400004i−4i000000000000000000000000000000000002-22i−2i
χ3444-444-4-4-400004i−4i00000000000000000000000000000000000-22−2i2i
χ3544-444-4-4-40000−4i4i000000000000000000000000000000000002-2−2i2i
χ3644-444-4-4-40000−4i4i00000000000000000000000000000000000-222i−2i
χ374-444-4-44-400040000000-400000004i−4i000000000000000000000000
χ384-444-4-44-400040000000-40000000−4i4i000000000000000000000000
χ394-444-4-44-4000-4000000040004-40000000000000000000000000000
χ404-444-4-44-4000-400000004000-440000000000000000000000000000
χ414-44-44-4-444000000000-400000000000000000000000000002i2−2i20000
χ424-44-44-4-444000000000-40000000000000000000000000000−2i22i20000
χ434-44-44-4-44-400000000040000000000000000000000000022−22000000
χ444-44-44-4-44-4000000000400000000000000000000000000−2222000000
χ454-4-44-44-44000000004-400000004-400000000000000000000000000
χ464-4-44-44-44000000004-40000000-4400000000000000000000000000
χ474-4-44-44-4400000000-440004-4000000000000000000000000000000
χ484-4-44-44-4400000000-44000-44000000000000000000000000000000
χ494-4-4-4444-404-400000000000000000002-200000002-2000000000000
χ504-4-4-4444-404-40000000000000000000-220000000-22000000000000
χ514-4-4-4444-40-4400000000000000000002-20000000-22000000000000
χ524-4-4-4444-40-440000000000000000000-2200000002-2000000000000
χ5388-8-8-8-888000000000000000000000000000000000000000000000

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