Finite Group Databasebeta

← Group #317310

Character table — Group #317310

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11112222444444444448888888888888161616161616161616161616161632323232
order12224444244448888884444888888888444444888888888888
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-11-1-111-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-111-111-1-1-1-1-1-1-1-111-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111-1-1-1-11-1-1-1-11111-111-111-1-1111111-1-1-1-1
χ61111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-11-1-1111111-1-111-1-1
χ91111111111111-1-1-1-1-1-11111-1-1-1-1-11111-11-1-11-11111-1-1-1-11-11-1
χ101111111111111-1-1-1-1-1-11111-1-1-1-1-11111-1-11-1-1111-1-111-1-1-11-11
χ111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-111111-1-11
χ121111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-11-1-111-1-111-111-1
χ131111111111111-1-1-1-1-1-1-1-1-1-1-11111111111-111-1-1-111-1-1-1-1-11-11
χ141111111111111-1-1-1-1-1-1-1-1-1-1-1111111111-111-11-1-1-1-111-1-11-11-1
χ151111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-11-111-1-11111-111-1
χ161111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-111111-1-1111-1-11
χ1722222222-2-22-2-22222-2-20000-2000022-2-20000000000002-20000
χ1822222222-2-22-2-22222-2-20000-20000-2-222000000000000-220000
χ1922222222-2-22-2-2-2-2-2-22200002000022-2-2000000000000-220000
χ2022222222-2-22-2-2-2-2-2-222000020000-2-2220000000000002-20000
χ21222222-2-222-2-2-222-2-2220000-200000000000000002i−2i2i−2i000000
χ22222222-2-222-2-2-222-2-2220000-20000000000000000−2i2i−2i2i000000
χ23222222-2-222-2-2-2-2-222-2-20000200000000000000002i−2i−2i2i000000
χ24222222-2-222-2-2-2-2-222-2-2000020000000000000000−2i2i2i−2i000000
χ25222222-2-2-2-2-22222-2-2-2-2000020000000002-20-22000000000000
χ26222222-2-2-2-2-22222-2-2-2-200002000000000-2202-2000000000000
χ27222222-2-2-2-2-222-2-222220000-2000000000220-2-2000000000000
χ28222222-2-2-2-2-222-2-222220000-2000000000-2-2022000000000000
χ292222-2-2-2-22-22-2200000022-2-2000002i−2i2i−2i0000002i−2i0000000000
χ302222-2-2-2-22-22-2200000022-2-200000−2i2i−2i2i000000−2i2i0000000000
χ312222-2-2-2-22-22-22000000-2-222000002i−2i2i−2i000000−2i2i0000000000
χ322222-2-2-2-22-22-22000000-2-22200000−2i2i−2i2i0000002i−2i0000000000
χ332222-2-2-2-2-2222-2000000000002i2i−2i−2i2i−2i−2i2i200-200000000000000
χ342222-2-2-2-2-2222-2000000000002i2i−2i−2i−2i2i2i−2i-200200000000000000
χ352222-2-2-2-2-2222-200000000000−2i−2i2i2i2i−2i−2i2i-200200000000000000
χ362222-2-2-2-2-2222-200000000000−2i−2i2i2i−2i2i2i−2i200-200000000000000
χ374444-4-4444-4-44-40000000000000000000000000000000000000
χ384444-4-444-44-4-440000000000000000000000000000000000000
χ394-4-44004i−4i000002i2−2i222−22002i−2i2-202ζ−2ζ2ζ3−2ζ30000000000000000000000
χ404-4-44004i−4i000002i2−2i222−2200−2i2i-220−2ζ2ζ−2ζ32ζ30000000000000000000000
χ414-4-44004i−4i00000−2i22i2−2222002i−2i2-20−2ζ2ζ−2ζ32ζ30000000000000000000000
χ424-4-44004i−4i00000−2i22i2−222200−2i2i-2202ζ−2ζ2ζ3−2ζ30000000000000000000000
χ434-4-4400−4i4i000002i2−2i2−2222002i−2i-220−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ444-4-4400−4i4i000002i2−2i2−222200−2i2i2-202ζ3−2ζ32ζ−2ζ0000000000000000000000
χ454-4-4400−4i4i00000−2i22i222−22002i−2i-2202ζ3−2ζ32ζ−2ζ0000000000000000000000
χ464-4-4400−4i4i00000−2i22i222−2200−2i2i2-20−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ4788-8-8000000000000042−420000000000000000000000000000000
χ4888-8-80000000000000−42420000000000000000000000000000000
χ498-88-88-800000000000000000000000000000000000000000000
χ508-88-8-8800000000000000000000000000000000000000000000

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