Finite Group Databasebeta

← Group #263270

Character table — Group #263270

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444444444444444448888161616161616161616161616161632323232
order12222244444444444444444488888888888888884444222244444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-11-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-11-111-1-11-1-1-1-111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-11-11-1-1-1-11-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1111-11-1-1-1-1-1-11-11
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-11111-111-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111-1-11
χ91111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-11-1-1-11-1111-1-1-11-11
χ101111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11-1-111-11-111-1-11-11-1
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111-1-11
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-111-1-111-111-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1111-111111-1-111-1-1-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-11-1-111-111-1-111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11111-1-1111-1-1-1-111
χ172222222-2-222-2-22-2-22222-2-2-2-2000000000000000022-2-22000-20000000000000
χ182222222-2-222-2-22-2-22222-2-2-2-20000000000000000-2-222-200020000000000000
χ192222222-2-222-2-22-2-2-2-2-2-22222000000000000000022-2-2-200020000000000000
χ202222222-2-222-2-22-2-2-2-2-2-222220000000000000000-2-2222000-20000000000000
χ21222222-222-2-222-2-2-200000000000000002222-2-2-2-22-22-20000000000002-20000
χ22222222-222-2-222-2-2-200000000000000002222-2-2-2-2-22-22000000000000-220000
χ23222222-222-2-222-2-2-20000000000000000-2-2-2-222222-22-2000000000000-220000
χ24222222-222-2-222-2-2-20000000000000000-2-2-2-22222-22-220000000000002-20000
χ25222222-2-2-2-2-2-2-2-222000000002i2i2i2i−2i−2i−2i−2i000000002-2-2200000000002i−2i000000
χ26222222-2-2-2-2-2-2-2-222000000002i2i2i2i−2i−2i−2i−2i00000000-222-20000000000−2i2i000000
χ27222222-2-2-2-2-2-2-2-22200000000−2i−2i−2i−2i2i2i2i2i000000002-2-220000000000−2i2i000000
χ28222222-2-2-2-2-2-2-2-22200000000−2i−2i−2i−2i2i2i2i2i00000000-222-200000000002i−2i000000
χ292222-2-22-2-2-2-22222-2000000000000000022-2-222-2-20000000202-200-200000000
χ302222-2-22-2-2-2-22222-2000000000000000022-2-222-2-20000000-20-2200200000000
χ312222-2-22-2-2-2-22222-20000000000000000-2-222-2-222000000020-2200-200000000
χ322222-2-22-2-2-2-22222-20000000000000000-2-222-2-2220000000-202-200200000000
χ332222-2-2-2-2-22222-2-22000000000000000022-2-2-2-22200000220000-2-2000000000
χ342222-2-2-2-2-22222-2-22000000000000000022-2-2-2-22200000-2-2000022000000000
χ352222-2-2-2-2-22222-2-220000000000000000-2-22222-2-2000002-20000-22000000000
χ362222-2-2-2-2-22222-2-220000000000000000-2-22222-2-200000-2200002-2000000000
χ374444-4-4444-4-4-4-44-440000000000000000000000000000000000000000000000
χ384444-4-4-44444-4-4-44-40000000000000000000000000000000000000000000000
χ3944-4-400000004-40002i2i−2i−2i2i2i−2i−2i22-2-222-2-200004i−4i000000000000000000000000
χ4044-4-400000004-40002i2i−2i−2i2i2i−2i−2i-2-222-2-2220000−4i4i000000000000000000000000
χ4144-4-400000004-4000−2i−2i2i2i−2i−2i2i2i22-2-222-2-20000−4i4i000000000000000000000000
χ4244-4-400000004-4000−2i−2i2i2i−2i−2i2i2i-2-222-2-22200004i−4i000000000000000000000000
χ4344-4-40000000-440002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000004-40000000000000000000000
χ4444-4-40000000-440002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000-440000000000000000000000
χ4544-4-40000000-44000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000-440000000000000000000000
χ4644-4-40000000-44000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000004-40000000000000000000000
χ474-44-40004i−4i00000002-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ322−222i2−2i200000000000000000000000000
χ484-44-40004i−4i00000002-22-22i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2222−2i22i200000000000000000000000000
χ494-44-40004i−4i0000000-22-22−2i2i−2i2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2222−2i22i200000000000000000000000000
χ504-44-40004i−4i0000000-22-22−2i2i−2i2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ322−222i2−2i200000000000000000000000000
χ514-44-4000−4i4i00000002-22-2−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−22222i2−2i200000000000000000000000000
χ524-44-4000−4i4i00000002-22-2−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ22−22−2i22i200000000000000000000000000
χ534-44-4000−4i4i0000000-22-222i−2i2i−2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ22−22−2i22i200000000000000000000000000
χ544-44-4000−4i4i0000000-22-222i−2i2i−2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−22222i2−2i200000000000000000000000000
χ554-4-444-44004-400-400000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ564-4-444-44004-400-40000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ574-4-444-4-400-44004000000000022−22−2222−222222−22000000000000000000000000000000
χ584-4-444-4-400-440040000000000−222222−2222−22−2222000000000000000000000000000000
χ594-4-44-44400-4400-4004i−4i−4i4i000000000000000000000000000000000000000000
χ604-4-44-44400-4400-400−4i4i4i−4i000000000000000000000000000000000000000000
χ614-4-44-44-4004-40040000004-4-4400000000000000000000000000000000000000
χ624-4-44-44-4004-4004000000-444-400000000000000000000000000000000000000

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