Finite Group Databasebeta

← Group #317255

Character table — Group #317255

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222444444444444488888888888888816161616161616161616161632323232
order12224444888824444888888882244888888888882224448888888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111-1-1-1-1111-1-1-1-11111-111-1111111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-11111111-1-11111-1-1-1-1-111-111-1-1-1-1-1-111-1-1
χ61111111111111111111-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ81111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111-1-1
χ911111111-1-1-1-111111-1-11111-1-11111-111-1-1-1-1-1-1-1-1-11-1-11-111-1-1111-11-1
χ1011111111-1-1-1-111111-1-11111-1-11111-111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-11-11
χ1111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1111111-1-1-1-111-111-111-1-1-1-1-11-11
χ1211111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1111111-1-1-1-11-111-11-1-111-1-11-11-1
χ1311111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-111-1-1-111-1-11-1-11
χ1411111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111111-111-1111-1-1-1-1-111-1
χ1511111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-11-1-1-11111-111-1
χ1611111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1111-1-1111-1-11
χ17222222222222-2-22-2-2222222-2-20000-2-2-2000022-2-20000000000000000
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
χ2022222222-2-2-2-2-2-22-2-2-2-2-2-2-2-2220000222000022-2-20000000000000000
χ2122222-2-22222222-2-2-2-2-20000220000-200000000000000002i−2i2i−2i000000
χ2222222-2-22222222-2-2-2-2-20000220000-20000000000000000−2i2i−2i2i000000
χ2322222-2-222222-2-2-222-2-20000-2-200002000000000002-20-220000000000
χ2422222-2-222222-2-2-222-2-20000-2-20000200000000000-2202-20000000000
χ2522222-2-22-2-2-2-222-2-2-2220000-2-20000200000000000000002i−2i−2i2i000000
χ2622222-2-22-2-2-2-222-2-2-2220000-2-2000020000000000000000−2i2i2i−2i000000
χ2722222-2-22-2-2-2-2-2-2-222220000220000-200000000000220-2-20000000000
χ2822222-2-22-2-2-2-2-2-2-222220000220000-200000000000-2-20220000000000
χ292222-2-2-2-200002-222-2002i2i−2i−2i0022-2-202i−2i0000000000000000002i−2i0000
χ302222-2-2-2-200002-222-2002i2i−2i−2i00-2-22202i−2i000000000000000000−2i2i0000
χ312222-2-2-2-200002-222-200−2i−2i2i2i0022-2-20−2i2i000000000000000000−2i2i0000
χ322222-2-2-2-200002-222-200−2i−2i2i2i00-2-2220−2i2i0000000000000000002i−2i0000
χ332222-2-2-2-20000-222-22002i2i−2i−2i0000000−2i2i2i2i−2i−2i0000200-2000000000000
χ342222-2-2-2-20000-222-22002i2i−2i−2i0000000−2i2i−2i−2i2i2i0000-2002000000000000
χ352222-2-2-2-20000-222-2200−2i−2i2i2i00000002i−2i2i2i−2i−2i0000-2002000000000000
χ362222-2-2-2-20000-222-2200−2i−2i2i2i00000002i−2i−2i−2i2i2i0000200-2000000000000
χ374444-444-400004-4-4-44000000000000000000000000000000000000000
χ384444-444-40000-44-44-4000000000000000000000000000000000000000
χ3944-4-404i−4i02i22i2−2i2−2i20000022−220000002-22i−2i0002ζ−2ζ2ζ3−2ζ300000000000000000000
χ4044-4-404i−4i02i22i2−2i2−2i20000022−22000000-22−2i2i000−2ζ2ζ−2ζ32ζ300000000000000000000
χ4144-4-404i−4i0−2i2−2i22i22i200000−22220000002-22i−2i000−2ζ2ζ−2ζ32ζ300000000000000000000
χ4244-4-404i−4i0−2i2−2i22i22i200000−2222000000-22−2i2i0002ζ−2ζ2ζ3−2ζ300000000000000000000
χ4344-4-40−4i4i02i22i2−2i2−2i200000−22220000002-2−2i2i0002ζ3−2ζ32ζ−2ζ00000000000000000000
χ4444-4-40−4i4i02i22i2−2i2−2i200000−2222000000-222i−2i000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ4544-4-40−4i4i0−2i2−2i22i22i20000022−220000002-2−2i2i000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ4644-4-40−4i4i0−2i2−2i22i22i20000022−22000000-222i−2i0002ζ3−2ζ32ζ−2ζ00000000000000000000
χ474-44-4400-44i−4i4i−4i00000002i2−2i22i2−2i2000000000000022−22000000000000000000
χ484-44-4400-44i−4i4i−4i0000000−2i22i2−2i22i20000000000000−2222000000000000000000
χ494-44-4400-4−4i4i−4i4i00000002i2−2i22i2−2i20000000000000−2222000000000000000000
χ504-44-4400-4−4i4i−4i4i0000000−2i22i2−2i22i2000000000000022−22000000000000000000
χ514-44-4-40040000000000022−22−22224-4000000000000022−220000000000000000
χ524-44-4-40040000000000022−22−2222-440000000000000−22220000000000000000
χ534-44-4-400400000000000−222222−224-40000000000000−22220000000000000000
χ544-44-4-400400000000000−222222−22-44000000000000022−220000000000000000
χ558-8-88000042−42−424200000000000000000000000000000000000000000000
χ568-8-880000−424242−4200000000000000000000000000000000000000000000

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