Finite Group Databasebeta

← Group #317259

Character table — Group #317259

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222444444444444488888888888888816161616161616161616161632323232
order12224444888824444888888882244888888888884444448888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1111-1-1-1-11111-1-11111-1-11111-1-1-1-1
χ41111111111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1
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
χ8111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1
χ911111111-1-1-1-111111-1-1-1-111111111-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11-11-1
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
χ1211111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1111-11-1
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
χ1411111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-111-1-111-1-1-111-1
χ1511111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111-111-1
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
χ212222-2-222222222-2-2-2-2-22200000000-20000000000000000002i−2i2i−2i0000
χ222222-2-222222222-2-2-2-2-22200000000-2000000000000000000−2i2i−2i2i0000
χ232222-2-2222222-2-2-222-2-2-2-20000000020000000000002-22-20000000000
χ242222-2-2222222-2-2-222-2-2-2-2000000002000000000000-22-220000000000
χ252222-2-222-2-2-2-222-2-2-222-2-20000000020000000000000000002i−2i−2i2i0000
χ262222-2-222-2-2-2-222-2-2-222-2-2000000002000000000000000000−2i2i2i−2i0000
χ272222-2-222-2-2-2-2-2-2-222222200000000-20000000000002-2-220000000000
χ282222-2-222-2-2-2-2-2-2-222222200000000-2000000000000-222-20000000000
χ292222-2-2-2-200002-22-2200002i2i−2i−2i22-2-202i−2i000000000000002i−2i00000000
χ302222-2-2-2-200002-22-2200002i2i−2i−2i-2-22202i−2i00000000000000−2i2i00000000
χ312222-2-2-2-200002-22-220000−2i−2i2i2i22-2-20−2i2i00000000000000−2i2i00000000
χ322222-2-2-2-200002-22-220000−2i−2i2i2i-2-2220−2i2i000000000000002i−2i00000000
χ332222-2-2-2-20000-2222-200002i2i−2i−2i00000−2i2i2i2i−2i−2i00002-200000000000000
χ342222-2-2-2-20000-2222-200002i2i−2i−2i00000−2i2i−2i−2i2i2i0000-2200000000000000
χ352222-2-2-2-20000-2222-20000−2i−2i2i2i000002i−2i2i2i−2i−2i0000-2200000000000000
χ362222-2-2-2-20000-2222-20000−2i−2i2i2i000002i−2i−2i−2i2i2i00002-200000000000000
χ37444444-4-400004-4-44-4000000000000000000000000000000000000000
χ38444444-4-40000-44-4-44000000000000000000000000000000000000000
χ394-44-4004-4000000000004-42i2−2i22i2−2i200000000000002i2−2i20000000000000000
χ404-44-4004-4000000000004-4−2i22i2−2i22i20000000000000−2i22i20000000000000000
χ414-44-4004-400000000000-442i2−2i22i2−2i20000000000000−2i22i20000000000000000
χ424-44-4004-400000000000-44−2i22i2−2i22i200000000000002i2−2i20000000000000000
χ434-44-400-444i4i−4i−4i00000000022−22−2222000000000002i2−2i2000000000000000000
χ444-44-400-444i4i−4i−4i000000000−222222−2200000000000−2i22i2000000000000000000
χ454-44-400-44−4i−4i4i4i00000000022−22−222200000000000−2i22i2000000000000000000
χ464-44-400-44−4i−4i4i4i000000000−222222−22000000000002i2−2i2000000000000000000
χ474-4-444i−4i002i2−2i22i2−2i20000022−220000002-22i−2i0002ζ3−2ζ32ζ−2ζ00000000000000000000
χ484-4-444i−4i002i2−2i22i2−2i20000022−22000000-22−2i2i000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ494-4-444i−4i00−2i22i2−2i22i200000−22220000002-22i−2i000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ504-4-444i−4i00−2i22i2−2i22i200000−2222000000-22−2i2i0002ζ3−2ζ32ζ−2ζ00000000000000000000
χ514-4-44−4i4i002i2−2i22i2−2i200000−22220000002-2−2i2i0002ζ−2ζ2ζ3−2ζ300000000000000000000
χ524-4-44−4i4i002i2−2i22i2−2i200000−2222000000-222i−2i000−2ζ2ζ−2ζ32ζ300000000000000000000
χ534-4-44−4i4i00−2i22i2−2i22i20000022−220000002-2−2i2i000−2ζ2ζ−2ζ32ζ300000000000000000000
χ544-4-44−4i4i00−2i22i2−2i22i20000022−22000000-222i−2i0002ζ−2ζ2ζ3−2ζ300000000000000000000
χ5588-8-8000042−42−424200000000000000000000000000000000000000000000
χ5688-8-80000−424242−4200000000000000000000000000000000000000000000

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