Finite Group Databasebeta

← Group #317260

Character table — Group #317260

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222444444444444488888888888888816161616161616161616161632323232
order12224444888824444888888882244888888888882444448888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-111-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1111-1-1-1-111111-1-1111-1-11111-1-1-1-1
χ41111111111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-111111-1-11111-1-1-1-11-1-1111-1-1-1-1-1-111-1-1
χ6111111111111111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-111-1-1-111111111-1-1
χ911111111-1-1-1-111111-1-1-1-111111111-111-1-1-1-1-1-1-1-11-1-11-1-11111-1-11-11-1
χ1011111111-1-1-1-111111-1-1-1-111111111-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-11
χ1111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-11-11
χ1211111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-111-111-1-1-1-1111-11-1
χ1311111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-11
χ1411111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-111-111-1-111-1-1-111-1
χ1511111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111-1-111-111-1
χ1611111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-11-1-11
χ17222222222222-2-22-2-222-2-222220000-2-2-2000022-2-20000000000000000
χ18222222222222-2-22-2-222-2-2-2-2-2-20000-2220000-2-2220000000000000000
χ1922222222-2-2-2-2-2-22-2-2-2-222222200002-2-20000-2-2220000000000000000
χ2022222222-2-2-2-2-2-22-2-2-2-222-2-2-2-20000222000022-2-20000000000000000
χ21222222-2-2222222-2-2-2-2-22200000000-20000000000000000002i−2i2i−2i0000
χ22222222-2-2222222-2-2-2-2-22200000000-2000000000000000000−2i2i−2i2i0000
χ23222222-2-22222-2-2-222-2-2-2-20000000020000000000200-22-20000000000
χ24222222-2-22222-2-2-222-2-2-2-20000000020000000000-2002-220000000000
χ25222222-2-2-2-2-2-222-2-2-222-2-20000000020000000000000000002i−2i−2i2i0000
χ26222222-2-2-2-2-2-222-2-2-222-2-2000000002000000000000000000−2i2i2i−2i0000
χ27222222-2-2-2-2-2-2-2-2-222222200000000-20000000000200-2-220000000000
χ28222222-2-2-2-2-2-2-2-2-222222200000000-20000000000-20022-20000000000
χ292222-2-2-2-200002-222-200002i2i−2i−2i22-2-202i−2i000000000000002i−2i00000000
χ302222-2-2-2-200002-222-200002i2i−2i−2i-2-22202i−2i00000000000000−2i2i00000000
χ312222-2-2-2-200002-222-20000−2i−2i2i2i22-2-20−2i2i00000000000000−2i2i00000000
χ322222-2-2-2-200002-222-20000−2i−2i2i2i-2-2220−2i2i000000000000002i−2i00000000
χ332222-2-2-2-20000-222-2200002i2i−2i−2i00000−2i2i2i2i−2i−2i000002-20000000000000
χ342222-2-2-2-20000-222-2200002i2i−2i−2i00000−2i2i−2i−2i2i2i00000-220000000000000
χ352222-2-2-2-20000-222-220000−2i−2i2i2i000002i−2i2i2i−2i−2i00000-220000000000000
χ362222-2-2-2-20000-222-220000−2i−2i2i2i000002i−2i−2i−2i2i2i000002-20000000000000
χ374444-4-44400004-4-4-44000000000000000000000000000000000000000
χ384444-4-4440000-44-44-4000000000000000000000000000000000000000
χ3944-4-4004i−4i2222−22−22000002i2−2i20000002-22i−2i0002ζ−2ζ2ζ3−2ζ300000000000000000000
χ4044-4-4004i−4i2222−22−22000002i2−2i2000000-22−2i2i000−2ζ2ζ−2ζ32ζ300000000000000000000
χ4144-4-4004i−4i−22−22222200000−2i22i20000002-22i−2i000−2ζ2ζ−2ζ32ζ300000000000000000000
χ4244-4-4004i−4i−22−22222200000−2i22i2000000-22−2i2i0002ζ−2ζ2ζ3−2ζ300000000000000000000
χ4344-4-400−4i4i2222−22−2200000−2i22i20000002-2−2i2i000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ4444-4-400−4i4i2222−22−2200000−2i22i2000000-222i−2i0002ζ3−2ζ32ζ−2ζ00000000000000000000
χ4544-4-400−4i4i−22−222222000002i2−2i20000002-2−2i2i0002ζ3−2ζ32ζ−2ζ00000000000000000000
χ4644-4-400−4i4i−22−222222000002i2−2i2000000-222i−2i000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ474-44-44-400000000000004-42i2−2i22i2−2i200000000000002i2−2i20000000000000000
χ484-44-44-400000000000004-4−2i22i2−2i22i20000000000000−2i22i20000000000000000
χ494-44-44-40000000000000-442i2−2i22i2−2i20000000000000−2i22i20000000000000000
χ504-44-44-40000000000000-44−2i22i2−2i22i200000000000002i2−2i20000000000000000
χ514-44-4-44004i−4i4i−4i00000000022−22−2222000000000002i2−2i2000000000000000000
χ524-44-4-44004i−4i4i−4i000000000−222222−2200000000000−2i22i2000000000000000000
χ534-44-4-4400−4i4i−4i4i00000000022−22−222200000000000−2i22i2000000000000000000
χ544-44-4-4400−4i4i−4i4i000000000−222222−22000000000002i2−2i2000000000000000000
χ558-8-8800004i2−4i2−4i24i200000000000000000000000000000000000000000000
χ568-8-880000−4i24i24i2−4i200000000000000000000000000000000000000000000

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