Finite Group Databasebeta

← Group #105056

Character table — Group #105056

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444444488888888888888888161616161616161616161616161616163232
order12222222222244444444444448888888888888888444444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ92222222222222222-2-222-2-2-2-2-2000000000000000022-2-200000000000000
χ102222222222222222-2-222-2-2-2-2-20000000000000000-2-22200000000000000
χ11222222222222-2-2-2-222-2-2-2-2-2-2200000000000000000000000000002i2i−2i−2i00
χ12222222222222-2-2-2-222-2-2-2-2-2-220000000000000000000000000000−2i−2i2i2i00
χ13222222222222-2-2-2-2-2-2-2-22222-2000000002222-2-2-2-2000000000000000000
χ14222222222222-2-2-2-2-2-2-2-22222-200000000-2-2-2-22222000000000000000000
χ1522222222-2-2-2-2222222-2-2-222-2-200000000000000000000000022-2-2000000
χ1622222222-2-2-2-2222222-2-2-222-2-2000000000000000000000000-2-222000000
χ1722222222-2-2-2-22222-2-2-2-22-2-222000000000000000000000000000000002-2
χ1822222222-2-2-2-22222-2-2-2-22-2-22200000000000000000000000000000000-22
χ1922222222-2-2-2-2-2-2-2-222222-2-22-2000000000000000000002i2i−2i−2i0000000000
χ2022222222-2-2-2-2-2-2-2-222222-2-22-200000000000000000000−2i−2i2i2i0000000000
χ2122222222-2-2-2-2-2-2-2-2-2-222-222-222i2i2i2i−2i−2i−2i−2i00000000000000000000000000
χ2222222222-2-2-2-2-2-2-2-2-2-222-222-22−2i−2i−2i−2i2i2i2i2i00000000000000000000000000
χ2322-2-22-22-222-2-200000000-22-220i2i2−i2−i2i2i2−i2−i2000022-2-200000000i2−i2i2−i2000000
χ2422-2-22-22-222-2-200000000-22-220i2i2−i2−i2i2i2−i2−i20000-2-22200000000−i2i2−i2i2000000
χ2522-2-22-22-222-2-200000000-22-220−i2−i2i2i2−i2−i2i2i2000022-2-200000000−i2i2−i2i2000000
χ2622-2-22-22-222-2-200000000-22-220−i2−i2i2i2−i2−i2i2i20000-2-22200000000i2−i2i2−i2000000
χ2722-2-22-22-2-2-2220000000022-2-2022−2−2−2−2222i2i−2i−2i000000000000i2−i2−i2i2000000
χ2822-2-22-22-2-2-2220000000022-2-2022−2−2−2−222−2i−2i2i2i000000000000−i2i2i2−i2000000
χ2922-2-22-22-2-2-2220000000022-2-20−2−22222−2−22i2i−2i−2i000000000000−i2i2i2−i2000000
χ3022-2-22-22-2-2-2220000000022-2-20−2−22222−2−2−2i−2i2i2i000000000000i2−i2−i2i2000000
χ312-2-2-222-222-2-2222-2-2002-200000000000002−22−22−22−2002i−2i00000000i2−i2i2−i200
χ322-2-2-222-222-2-2222-2-2002-200000000000002−22−22−22−200−2i2i00000000−i2i2−i2i200
χ332-2-2-222-222-2-2222-2-2002-20000000000000−22−22−22−22002i−2i00000000−i2i2−i2i200
χ342-2-2-222-222-2-2222-2-2002-20000000000000−22−22−22−2200−2i2i00000000i2−i2i2−i200
χ352-2-2-222-222-2-22-2-22200-2200000000000002−22−2−22−222-200000000002−2−2200
χ362-2-2-222-222-2-22-2-22200-2200000000000002−22−2−22−22-220000000000−222−200
χ372-2-2-222-222-2-22-2-22200-220000000000000−22−222−22−22-20000000000−222−200
χ382-2-2-222-222-2-22-2-22200-220000000000000−22−222−22−2-2200000000002−2−2200
χ39444-4-4-4-4400004-44-4000000000000000000000000000002-22-20000000000
χ40444-4-4-4-4400004-44-400000000000000000000000000000-22-220000000000
χ41444-4-4-4-440000-44-44000000000000000000000000000002i−2i−2i2i0000000000
χ42444-4-4-4-440000-44-4400000000000000000000000000000−2i2i2i−2i0000000000
χ4344-4-44-44-444-4-4000000004-44-400000000000000000000000000000000000
χ4444-4-44-44-4-4-44400000000-4-44400000000000000000000000000000000000
χ454-4444-4-4-44-44-4000000000000000000000000022−22−2222000000000000000000
χ464-4444-4-4-44-44-40000000000000000000000000−222222−22000000000000000000
χ474-4444-4-4-4-44-440000000000000000000002i2−2i2−2i22i20000000000000000000000
χ484-4444-4-4-4-44-44000000000000000000000−2i22i22i2−2i20000000000000000000000
χ494-44-4-444-4000000004i−4i00000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000
χ504-44-4-444-4000000004i−4i0000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000
χ514-44-4-444-400000000−4i4i00000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000
χ524-44-4-444-400000000−4i4i0000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000
χ534-4-44-4-44400004-4-440000000002-2-222-2-2200000000000000000000000000
χ544-4-44-4-44400004-4-44000000000-222-2-222-200000000000000000000000000
χ554-4-44-4-4440000-444-40000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ564-4-44-4-4440000-444-4000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ574-4-4-444-44-444-444-4-400-44000000000000000000000000000000000000000
χ584-4-4-444-44-444-4-4-444004-4000000000000000000000000000000000000000
χ5988-88-88-8-8000000000000000000000000000000000000000000000000000

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