Finite Group Databasebeta

← Group #263248

Character table — Group #263248

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222224444444444888888888888888816161616161616161616161632323232
order12222244444444444444888844444488888888882444444444888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ811111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-111-1-111-1-1-1-11-11-1
χ1011111111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-11-11
χ1111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-11-11
χ1211111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111111-11-1
χ1311111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111111-1-11
χ1411111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-111-1
χ1511111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-111-1
χ1611111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11111-1-1-1-11-1-11
χ17222222222-2-2-2-2222-2-2-2-222222-200000000-2-222-2-20000000000000000
χ18222222222-2-2-2-2222-2-2-2-2-2-2-2-22-20000000022-2-2220000000000000000
χ19222222222-2-2-2-22-2-222-2-22222-2200000000-2-2-2-2220000000000000000
χ20222222222-2-2-2-22-2-222-2-2-2-2-2-2-22000000002222-2-20000000000000000
χ21222222-2-2-22222-22222-2-20000-2-222-2-200000000002-200000000000000
χ22222222-2-2-22222-22222-2-20000-2-2-2-2220000000000-2200000000000000
χ23222222-2-2-22222-2-2-2-2-2-2-200002222-2-20000000000-2200000000000000
χ24222222-2-2-22222-2-2-2-2-2-2-2000022-2-22200000000002-200000000000000
χ25222222-2-2-2-2-2-2-2-222-2-2220000-2200002i2i−2i−2i00000000000000002i−2i0000
χ26222222-2-2-2-2-2-2-2-222-2-2220000-220000−2i−2i2i2i0000000000000000−2i2i0000
χ27222222-2-2-2-2-2-2-2-2-2-2222200002-200002i2i−2i−2i0000000000000000−2i2i0000
χ28222222-2-2-2-2-2-2-2-2-2-2222200002-20000−2i−2i2i2i00000000000000002i−2i0000
χ292222-2-22-2-222-2-2200002-222-2-200000000002-2000000002-2002-2000000
χ302222-2-22-2-222-2-2200002-222-2-200000000002-200000000-2200-22000000
χ312222-2-22-2-222-2-2200002-2-2-2220000000000-22000000002-200-22000000
χ322222-2-22-2-222-2-2200002-2-2-2220000000000-2200000000-22002-2000000
χ332222-2-22-2-2-2-22220000-2222-2-20000000000-220000002-2002-200000000
χ342222-2-22-2-2-2-22220000-2222-2-20000000000-22000000-2200-2200000000
χ352222-2-22-2-2-2-22220000-22-2-22200000000002-20000002-200-2200000000
χ362222-2-22-2-2-2-22220000-22-2-22200000000002-2000000-22002-200000000
χ374444-4-4-44444-4-4-40000-44000000000000000000000000000000000000
χ384444-4-4-444-4-444-400004-4000000000000000000000000000000000000
χ3944-4-44-40004-44-40000000000000000000000022−2222−220000000000000000
χ4044-4-44-40004-44-400000000000000000000000−2222−22220000000000000000
χ4144-4-44-4000-44-440000000000000000000000022−22−22220000000000000000
χ4244-4-44-4000-44-4400000000000000000000000−222222−220000000000000000
χ4344-4-4-440004-4-4404-44-400000000000000000000000000000000000000
χ4444-4-4-440004-4-440-44-4400000000000000000000000000000000000000
χ4544-4-4-44000-444-404-4-4400000000000000000000000000000000000000
χ4644-4-4-44000-444-40-444-400000000000000000000000000000000000000
χ474-44-40004i−4i000000000002i2−2i222−22002i−2i2-22ζ−2ζ2ζ3−2ζ30000000000000000000000
χ484-44-40004i−4i000000000002i2−2i222−2200−2i2i-22−2ζ2ζ−2ζ32ζ30000000000000000000000
χ494-44-40004i−4i00000000000−2i22i2−2222002i−2i2-2−2ζ2ζ−2ζ32ζ30000000000000000000000
χ504-44-40004i−4i00000000000−2i22i2−222200−2i2i-222ζ−2ζ2ζ3−2ζ30000000000000000000000
χ514-44-4000−4i4i000000000002i2−2i2−2222002i−2i-22−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ524-44-4000−4i4i000000000002i2−2i2−222200−2i2i2-22ζ3−2ζ32ζ−2ζ0000000000000000000000
χ534-44-4000−4i4i00000000000−2i22i222−22002i−2i-222ζ3−2ζ32ζ−2ζ0000000000000000000000
χ544-44-4000−4i4i00000000000−2i22i222−2200−2i2i2-2−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ558-8-88008000000-8000000000000000000000000000000000000000000
χ568-8-8800-80000008000000000000000000000000000000000000000000

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