Finite Group Databasebeta

← Group #263254

Character table — Group #263254

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222224444444444888888888888888816161616161616161616161632323232
order12222244444444444444888844444488888888882244444444888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ711111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-111
χ811111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1
χ91111111111111111-1-1-1-11111-1-11111111111-1-1-1-11-11-1-1-11-11-1-1-11-11-1
χ101111111111111111-1-1-1-11111-1-11111111111-1-1-1-1-11-11-1-1-11-11-1-1-11-11
χ111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11-1111-11-111-11-11
χ121111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1111-11-11111-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-11-1-11-1-11111-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-111-1-1-1-111-111-111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-11111-1-11-1-1-111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-111-111-111-1-1-11-1-11
χ1722222222-2-2-2-222-2-222220000-2-222-2-2000000000000002-20000000000
χ1822222222-2-2-2-222-2-222220000-2-2-2-22200000000000000-220000000000
χ1922222222-2-2-2-222-2-2-2-2-2-200002222-2-200000000000000-220000000000
χ2022222222-2-2-2-222-2-2-2-2-2-2000022-2-222000000000000002-20000000000
χ21222222-2-22222-2-2-2-222-2-222222-200000000-2-222-2-20000000000000000
χ22222222-2-22222-2-2-2-222-2-2-2-2-2-22-20000000022-2-2220000000000000000
χ23222222-2-22222-2-2-2-2-2-2222222-2200000000-2-2-2-2220000000000000000
χ24222222-2-22222-2-2-2-2-2-222-2-2-2-2-22000000002222-2-20000000000000000
χ25222222-2-2-2-2-2-2-2-22222-2-20000-2200002i2i−2i−2i00000000000000002i−2i0000
χ26222222-2-2-2-2-2-2-2-22222-2-20000-220000−2i−2i2i2i0000000000000000−2i2i0000
χ27222222-2-2-2-2-2-2-2-222-2-22200002-200002i2i−2i−2i0000000000000000−2i2i0000
χ28222222-2-2-2-2-2-2-2-222-2-22200002-20000−2i−2i2i2i00000000000000002i−2i0000
χ292222-2-22-2-2-2222-22-2000022-2-200000000002-200000202000-20-2000000
χ302222-2-22-2-2-2222-22-2000022-2-200000000002-200000-20-2000202000000
χ312222-2-22-2-2-2222-22-20000-2-2220000000000-220000020-2000-202000000
χ322222-2-22-2-2-2222-22-20000-2-2220000000000-2200000-20200020-2000000
χ332222-2-2-22-2-222-22-22000022-2-20000000000-220000202000-20-20000000
χ342222-2-2-22-2-222-22-22000022-2-20000000000-220000-20-20002020000000
χ352222-2-2-22-2-222-22-220000-2-22200000000002-2000020-2000-2020000000
χ362222-2-2-22-2-222-22-220000-2-22200000000002-20000-20200020-20000000
χ374444-4-44-444-4-44-4-440000000000000000000000000000000000000000
χ384444-4-4-4444-4-4-444-40000000000000000000000000000000000000000
χ394-44-400004i−4i00000000002i2−2i222−22002-22i−2i2ζ−2ζ2ζ3−2ζ30000000000000000000000
χ404-44-400004i−4i00000000002i2−2i222−2200-22−2i2i−2ζ2ζ−2ζ32ζ30000000000000000000000
χ414-44-400004i−4i0000000000−2i22i2−2222002-22i−2i−2ζ2ζ−2ζ32ζ30000000000000000000000
χ424-44-400004i−4i0000000000−2i22i2−222200-22−2i2i2ζ−2ζ2ζ3−2ζ30000000000000000000000
χ434-44-40000−4i4i00000000002i2−2i2−2222002-2−2i2i2ζ3−2ζ32ζ−2ζ0000000000000000000000
χ444-44-40000−4i4i00000000002i2−2i2−222200-222i−2i−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ454-44-40000−4i4i0000000000−2i22i222−22002-2−2i2i−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ464-44-40000−4i4i0000000000−2i22i222−2200-222i−2i2ζ3−2ζ32ζ−2ζ0000000000000000000000
χ474-4-444-4440000-4-4004-44-4000000000000000000000000000000000000
χ484-4-444-4440000-4-400-44-44000000000000000000000000000000000000
χ494-4-444-4-4-4000044004-4-44000000000000000000000000000000000000
χ504-4-444-4-4-400004400-444-4000000000000000000000000000000000000
χ514-4-44-444-40000-4400000000000000000000002i2−2i22i2−2i20000000000000000
χ524-4-44-444-40000-440000000000000000000000−2i22i2−2i22i20000000000000000
χ534-4-44-44-4400004-400000000000000000000002i2−2i2−2i22i20000000000000000
χ544-4-44-44-4400004-40000000000000000000000−2i22i22i2−2i20000000000000000
χ5588-8-80000008-800000000000000000000000000000000000000000000
χ5688-8-8000000-8800000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.