Finite Group Databasebeta

← Group #337618

Character table — Group #337618

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111111112222222244888888888888888816161616161616161616161616161616323232
order12222222444444444444448888888888882444444488888888444
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-1111-1111-111-1-1-1-1-1-1-11-1
χ31111111111111111111111-1-1-1-11111-1-1-1-1-11111-111-1-1-1-111-1-1-1-11
χ41111111111111111111111-1-1-1-1-1-1-1-11111-111-11-11-1-1-111-1-1111-1-1
χ511111111111111111111-1-1111111111111-1-1-111-1-111111-1-1-1-1-1-1-1
χ611111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111111-11
χ711111111111111111111-1-1-1-1-1-11111-1-1-1-11-1-1111-11-1-1-1-1-1-11111-1
χ811111111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-1-1-11111-1-1-111
χ9111111111111111111-1-1111111111111111-1-1-1-111-1-1-1-1-11111-1-1-1
χ10111111111111111111-1-1111111-1-1-1-1-1-1-1-11-1-11-1111-1-111-1-1-1-11-11
χ11111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1111111-1-111-1
χ12111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-11-1-11111-1-1-1-111-111
χ13111111111111111111-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ14111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-11-1-1111111-11-1
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11-1-11111-1-111-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-111-1-11-1-1
χ172222222222-2-2-2-222-2-22200000022-2-200000002-200-200000000000
χ182222222222-2-2-2-222-2-222000000-2-2220000000-2-200200000000000
χ192222222222-2-2-2-222-2-2-2-200000022-2-20000000-2200200000000000
χ202222222222-2-2-2-222-2-2-2-2000000-2-22200000002200-200000000000
χ2122222222-2-22222-2-2-2-2002222-2-20000000020000-2-2000000000000
χ2222222222-2-22222-2-2-2-20022-2-22200000000-200002-2000000000000
χ2322222222-2-22222-2-2-2-200-2-222-2-200000000-2000022000000000000
χ2422222222-2-22222-2-2-2-200-2-2-2-2220000000020000-22000000000000
χ2522-2-222-2-2-2-222-2-2222-2000000000000000002i−2i00000002i−2i002-2000
χ2622-2-222-2-2-2-222-2-2222-2000000000000000002i−2i0000000−2i2i00-22000
χ2722-2-222-2-2-2-222-2-2222-200000000000000000−2i2i00000002i−2i00-22000
χ2822-2-222-2-2-2-222-2-2222-200000000000000000−2i2i0000000−2i2i002-2000
χ2944444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000
χ3044-4-444-4-44444-4-4-4-4-4400000000000000000000000000000000000
χ3144-4-444-4-444-4-444-4-44-400000000000000000000000000000000000
χ3244-4-444-4-4-4-4-4-44444-4400000000000000000000000000000000000
χ3344-4-4-4-444000000000000002i2−2i2002i2−2i20022-2-20000000000000000000
χ3444-4-4-4-444000000000000002i2−2i200−2i22i200-2-2220000000000000000000
χ3544-4-4-4-44400000000000000−2i22i2002i2−2i200-2-2220000000000000000000
χ3644-4-4-4-44400000000000000−2i22i200−2i22i20022-2-20000000000000000000
χ374-44-44-44-4004-44-400000000004i−4i000000000000000000000000000
χ384-44-44-44-4004-44-40000000000−4i4i000000000000000000000000000
χ394-44-44-44-400-44-4400000000000000002i2−2i22i2−2i20000000000000000000
χ404-44-44-44-400-44-440000000000000000−2i22i2−2i22i20000000000000000000
χ414-44-4-44-444-400004-4000000000000000000000000002i2−2i2000000000
χ424-44-4-44-444-400004-400000000000000000000000000−2i22i2000000000
χ434-44-4-44-44-440000-44004i−4i000000000000000000000000000000000
χ444-44-4-44-44-440000-4400−4i4i000000000000000000000000000000000
χ454-4-444-4-44004-4-44000000000000000000000000000000002i2−2i200000
χ464-4-444-4-44004-4-4400000000000000000000000000000000−2i22i200000
χ474-4-444-4-4400-444-40000004i−4i0000000000000000000000000000000
χ484-4-444-4-4400-444-4000000−4i4i0000000000000000000000000000000
χ494-4-44-444-44-40000-44000000000000002i2−2i2−2i22i20000000000000000000
χ504-4-44-444-44-40000-4400000000000000−2i22i22i2−2i20000000000000000000
χ514-4-44-444-4-4400004-40000000000004i−4i00000000000000000000000
χ524-4-44-444-4-4400004-4000000000000−4i4i00000000000000000000000
χ538888-8-8-8-8000000000000000000000000000000000000000000000

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