Finite Group Databasebeta

← Group #265321

Character table — Group #265321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222244444444444444448888888888888816161616161616161616161632323232
order12222244442222444488888888444444888888882222444444888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ7111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-111
χ8111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1
χ9111111111111-1-1-1-11111111111-1-11111-1-11111-1-11-11-1-1-11-11-1-1-11-11-1
χ10111111111111-1-1-1-11111111111-1-11111-1-11111-1-1-11-11-1-1-11-11-1-1-11-11
χ11111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111-11-111-11-11
χ12111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-11-11111-11-1
χ13111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11-1-11-1-11111-1-11
χ14111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-111-1-1-1-111-111-111-1
χ15111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11111-1-11-1-1-111-1
χ16111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-111-1-1-11-1-11
χ172222222222-2-222-2-2-2-22222-2-2-2-22-20000220000-2-20000000000000000
χ182222222222-2-222-2-2-2-2-2-2-2-222222-20000-2-20000220000000000000000
χ192222222222-2-2-2-222-2-22222-2-2-2-2-220000-2-20000220000000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-22222-220000220000-2-20000000000000000
χ21222222-2-2-2-2222222-2-200000000-2-20000002i2i−2i−2i0000000000002i−2i0000
χ22222222-2-2-2-2222222-2-200000000-2-2000000−2i−2i2i2i000000000000−2i2i0000
χ23222222-2-2-2-222-2-2-2-2-2-200000000220000002i2i−2i−2i000000000000−2i2i0000
χ24222222-2-2-2-222-2-2-2-2-2-20000000022000000−2i−2i2i2i0000000000002i−2i0000
χ25222222-2-2-2-2-2-222-2-22200000000-2222-2-20000000000002-20000000000
χ26222222-2-2-2-2-2-222-2-22200000000-22-2-222000000000000-220000000000
χ27222222-2-2-2-2-2-2-2-22222000000002-222-2-2000000000000-220000000000
χ28222222-2-2-2-2-2-2-2-22222000000002-2-2-2220000000000002-20000000000
χ292222-2-22-2-222-200002-222-2-222-2-2000000000000000202000-20-2000000
χ302222-2-22-2-222-200002-222-2-222-2-2000000000000000-20-2000202000000
χ312222-2-22-2-222-200002-2-2-222-2-22200000000000000020-2000-202000000
χ322222-2-22-2-222-200002-2-2-222-2-222000000000000000-20200020-2000000
χ332222-2-22-2-22-220000-2222-2-2-2-2220000000000000020-2000-2020000000
χ342222-2-22-2-22-220000-2222-2-2-2-22200000000000000-20200020-20000000
χ352222-2-22-2-22-220000-22-2-22222-2-200000000000000202000-20-20000000
χ362222-2-22-2-22-220000-22-2-22222-2-200000000000000-20-20002020000000
χ374444-4-4-444-44-40000-4400000000000000000000000000000000000000
χ384444-4-4-444-4-4400004-400000000000000000000000000000000000000
χ3944-4-40004i−4i000000000000022−222i2−2i2002-22i−2i002ζ−2ζ2ζ3−2ζ3000000000000000000
χ4044-4-40004i−4i000000000000022−222i2−2i200-22−2i2i00−2ζ2ζ−2ζ32ζ3000000000000000000
χ4144-4-40004i−4i0000000000000−2222−2i22i2002-22i−2i00−2ζ2ζ−2ζ32ζ3000000000000000000
χ4244-4-40004i−4i0000000000000−2222−2i22i200-22−2i2i002ζ−2ζ2ζ3−2ζ3000000000000000000
χ4344-4-4000−4i4i000000000000022−22−2i22i2002-2−2i2i00−2ζ32ζ3−2ζ2ζ000000000000000000
χ4444-4-4000−4i4i000000000000022−22−2i22i200-222i−2i002ζ3−2ζ32ζ−2ζ000000000000000000
χ4544-4-4000−4i4i0000000000000−22222i2−2i2002-2−2i2i002ζ3−2ζ32ζ−2ζ000000000000000000
χ4644-4-4000−4i4i0000000000000−22222i2−2i200-222i−2i00−2ζ32ζ3−2ζ2ζ000000000000000000
χ474-4-444-4000000004-40022−2222−22000000000000000022−220000000000000000
χ484-4-444-4000000004-400−2222−22220000000000000000−22220000000000000000
χ494-4-444-400000000-440022−2222−220000000000000000−22220000000000000000
χ504-4-444-400000000-4400−2222−2222000000000000000022−220000000000000000
χ514-4-44-440000004-4000022−22−2222000000000022−220000000000000000000000
χ524-4-44-440000004-40000−222222−220000000000−22220000000000000000000000
χ534-4-44-44000000-44000022−22−22220000000000−22220000000000000000000000
χ544-4-44-44000000-440000−222222−22000000000022−220000000000000000000000
χ558-88-800800-80000000000000000000000000000000000000000000000
χ568-88-800-80080000000000000000000000000000000000000000000000

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