Finite Group Databasebeta

← Group #317041

Character table — Group #317041

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222222244444448888888888888888816161616161616161616161632323232
order12222244444488884448888224488888888888882244448888884488
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-11-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111-1-1-1-1-1111-11-1-1-1-1-1-111-1-1
χ41111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111-1-1-1-111111-1-1-1-11111-1111-111111-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ811111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-111111111-1-1
χ9111111111111-1-1-1-1111-1-1-1-11111-11111-1-1-1-1-1-1-1-1-111-1-1-111-1-1111-11-1
χ10111111111111-1-1-1-1111-1-1-1-11111-11111-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-11-11
χ11111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-11111111-11-1-1-111-1-11-1-11
χ12111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-111111-1-1-1-1-111-1
χ13111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-11-111-1-1-1-1-11-11
χ14111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-111-1-11-11-1
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1-1-11111-111-1
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11-1111-1-1111-1-11
χ17222222222-2-222222-2-2-2-2-2220000-200000000000002-220-20000000000
χ18222222222-2-222222-2-2-2-2-2220000-20000000000000-22-2020000000000
χ19222222222-2-22-2-2-2-2-2-2-222-2-20000200000000000002-2-2020000000000
χ20222222222-2-22-2-2-2-2-2-2-222-2-2000020000000000000-2220-20000000000
χ21222222-2-2-2-2-2-200002-22000022-2-202i2i−2i−2i0000000000000000002i−2i0000
χ22222222-2-2-2-2-2-200002-22000022-2-20−2i−2i2i2i000000000000000000−2i2i0000
χ23222222-2-2-2-2-2-200002-220000-2-22202i2i−2i−2i000000000000000000−2i2i0000
χ24222222-2-2-2-2-2-200002-220000-2-2220−2i−2i2i2i0000000000000000002i−2i0000
χ252222-2-22-2-22222222-2-2222-2-20000-22-22-2000022-2-20000000000000000
χ262222-2-22-2-22222222-2-2222-2-20000-2-22-220000-2-2220000000000000000
χ272222-2-22-2-2222-2-2-2-2-2-22-2-222000022-22-20000-2-2220000000000000000
χ282222-2-22-2-2222-2-2-2-2-2-22-2-22200002-22-22000022-2-20000000000000000
χ292222-2-22-2-2-2-22222222-2-2-2-2-2000020000000000000000002i−2i2i−2i000000
χ302222-2-22-2-2-2-22222222-2-2-2-2-200002000000000000000000−2i2i−2i2i000000
χ312222-2-22-2-2-2-22-2-2-2-222-222220000-20000000000000000002i−2i−2i2i000000
χ322222-2-22-2-2-2-22-2-2-2-222-222220000-2000000000000000000−2i2i2i−2i000000
χ332222-2-2-222-2-2-20000-2220000000002i−2i−2i2i2i2i−2i−2i00002000-200000000000
χ342222-2-2-222-2-2-20000-2220000000002i−2i−2i2i−2i−2i2i2i0000-2000200000000000
χ352222-2-2-222-2-2-20000-222000000000−2i2i2i−2i2i2i−2i−2i0000-2000200000000000
χ362222-2-2-222-2-2-20000-222000000000−2i2i2i−2i−2i−2i2i2i00002000-200000000000
χ37444444-4-4-444-40000-44-40000000000000000000000000000000000000
χ384444-4-4-44444-400004-4-40000000000000000000000000000000000000
χ3944-4-4000004i−4i02222−22−220002i2−2i2002-22i−2i000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ4044-4-4000004i−4i02222−22−220002i2−2i200-22−2i2i00000−2ζ2ζ−2ζ32ζ300000000000000000000
χ4144-4-4000004i−4i0−22−222222000−2i22i2002-22i−2i00000−2ζ2ζ−2ζ32ζ300000000000000000000
χ4244-4-4000004i−4i0−22−222222000−2i22i200-22−2i2i000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ4344-4-400000−4i4i02222−22−22000−2i22i2002-2−2i2i00000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ4444-4-400000−4i4i02222−22−22000−2i22i200-222i−2i000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ4544-4-400000−4i4i0−22−2222220002i2−2i2002-2−2i2i000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ4644-4-400000−4i4i0−22−2222220002i2−2i200-222i−2i00000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ474-4-444-444-400-44i−4i4i−4i000004i−4i000000000000000000000000000000000
χ484-4-444-444-400-4−4i4i−4i4i00000−4i4i000000000000000000000000000000000
χ494-4-444-4-4-4400400000000000000000000000022−2222−220000000000000000
χ504-4-444-4-4-44004000000000000000000000000−2222−22220000000000000000
χ514-4-44-444-4400-44i−4i4i−4i00000−4i4i000000000000000000000000000000000
χ524-4-44-444-4400-4−4i4i−4i4i000004i−4i000000000000000000000000000000000
χ534-4-44-44-44-400400000000000000000000000022−22−22220000000000000000
χ544-4-44-44-44-4004000000000000000000000000−222222−220000000000000000
χ558-88-8000000004i2−4i2−4i24i20000000000000000000000000000000000000000
χ568-88-800000000−4i24i24i2−4i20000000000000000000000000000000000000000

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