Finite Group Databasebeta

← Group #105161

Character table — Group #105161

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444444488888888888888888161616161616161616161616161616163232
order12222222444444444444444448888888888888888224488888888888844
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ92222222222222222-2-2-2-22-2-22-20000000000000000000022-2-20000000000
χ102222222222222222-2-2-2-22-2-22-200000000000000000000-2-2220000000000
χ11222222222-2-2-2-2222222-2-22-2-2-2000000000000000022-2-200000000000000
χ12222222222-2-2-2-2222222-2-22-2-2-20000000000000000-2-22200000000000000
χ13222222222-2-2-2-2222-2-2-22-2-22-22000000000000000000000000000000002-2
χ14222222222-2-2-2-2222-2-2-22-2-22-2200000000000000000000000000000000-22
χ1522222222-22222-2-2-222-22-2-22-2-200000000000000000000000000002i2i−2i−2i00
χ1622222222-22222-2-2-222-22-2-22-2-20000000000000000000000000000−2i−2i2i2i00
χ1722222222-22222-2-2-2-2-22-2-22-2-22000000002i2i2i2i−2i−2i−2i−2i000000000000000000
χ1822222222-22222-2-2-2-2-22-2-22-2-2200000000−2i−2i−2i−2i2i2i2i2i000000000000000000
χ1922222222-2-2-2-2-2-2-2-222-2-22-2-2220000000000000000000000002i2i−2i−2i000000
χ2022222222-2-2-2-2-2-2-2-222-2-22-2-222000000000000000000000000−2i−2i2i2i000000
χ2122222222-2-2-2-2-2-2-2-2-2-2222222-22222-2-2-2-200000000000000000000000000
χ2222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2222200000000000000000000000000
χ232222-2-2-2-220000-2-222-2-2002000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22-20000000000000000
χ242222-2-2-2-220000-2-222-2-2002000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-220000000000000000
χ252222-2-2-2-220000-2-222-2-2002000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-220000000000000000
χ262222-2-2-2-220000-2-222-2-2002000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22-20000000000000000
χ272222-2-2-2-2-2000022-2-22-2002000i2i2−i2−i2−i2−i2i2i222−2−2−2−222002i−2i00000000000000
χ282222-2-2-2-2-2000022-2-22-2002000i2i2−i2−i2−i2−i2i2i2−2−22222−2−200−2i2i00000000000000
χ292222-2-2-2-2-2000022-2-22-2002000−i2−i2i2i2i2i2−i2−i222−2−2−2−22200−2i2i00000000000000
χ302222-2-2-2-2-2000022-2-22-2002000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2002i−2i00000000000000
χ3122-2-2-2-222222-2-22-2-20000200-2000000000i2−i2i2−i2i2−i2i2−i20000002-20000i2−i2i2−i200
χ3222-2-2-2-222222-2-22-2-20000200-2000000000i2−i2i2−i2i2−i2i2−i2000000-220000−i2i2−i2i200
χ3322-2-2-2-222222-2-22-2-20000200-2000000000−i2i2−i2i2−i2i2−i2i20000002-20000−i2i2−i2i200
χ3422-2-2-2-222222-2-22-2-20000200-2000000000−i2i2−i2i2−i2i2−i2i2000000-220000i2−i2i2−i200
χ3522-2-2-2-222-222-2-2-2220000-20020000000002−22−2−22−2200002-20000002−2−2200
χ3622-2-2-2-222-222-2-2-2220000-20020000000002−22−2−22−220000-22000000−222−200
χ3722-2-2-2-222-222-2-2-2220000-2002000000000−22−222−22−200002-2000000−222−200
χ3822-2-2-2-222-222-2-2-2220000-2002000000000−22−222−22−20000-220000002−2−2200
χ394444-4-4-4-440000-4-44-44400-40000000000000000000000000000000000000
χ404444-4-4-4-4-4000044-44-4400-40000000000000000000000000000000000000
χ4144-4-444-4-440000-44-4000000000000000002-2-222-2-22000000000000000000
χ4244-4-444-4-440000-44-400000000000000000-222-2-222-2000000000000000000
χ4344-4-444-4-4-400004-44000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ4444-4-444-4-4-400004-4400000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ4544-4-4-4-4444-4-4444-4-40000-400400000000000000000000000000000000000
χ4644-4-4-4-444-4-4-444-4440000400-400000000000000000000000000000000000
χ474-44-44-44-404i−4i4i−4i0000000000002-22-22i−2i2i−2i00000000000000000000000000
χ484-44-44-44-404i−4i4i−4i000000000000-22-22−2i2i−2i2i00000000000000000000000000
χ494-44-44-44-40−4i4i−4i4i0000000000002-22-2−2i2i−2i2i00000000000000000000000000
χ504-44-44-44-40−4i4i−4i4i000000000000-22-222i−2i2i−2i00000000000000000000000000
χ514-44-4-44-4400000000000400-4002i2−2i2−2i22i2000000000000000000000000000000
χ524-44-4-44-4400000000000400-400−2i22i22i2−2i2000000000000000000000000000000
χ534-44-4-44-4400000000000-400400000022−22−222200000000000000000000000000
χ544-44-4-44-4400000000000-4004000000−222222−2200000000000000000000000000
χ554-4-44-444-404i−4i−4i4i0000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3000000
χ564-4-44-444-404i−4i−4i4i000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3000000
χ574-4-44-444-40−4i4i4i−4i0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ000000
χ584-4-44-444-40−4i4i4i−4i000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ000000
χ598-8-888-8-88000000000000000000000000000000000000000000000000000

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