Finite Group Databasebeta

← Group #104178

Character table — Group #104178

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444444488888888888888888161616161616161616161616161616163232
order12222222222244444444444444444444488888888444444448888888844
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
χ9222222222222222222-2-2-2-2-2-2-2000000000000000022-2-200000000000000
χ10222222222222222222-2-2-2-2-2-2-20000000000000000-2-22200000000000000
χ11222222222222-2-2-2-2-2-2222-2-22-22222-2-2-2-200000000000000000000000000
χ12222222222222-2-2-2-2-2-2222-2-22-2-2-2-2-2222200000000000000000000000000
χ13222222222222-2-2-2-2-2-2-2-2-222-220000000000000000000022-2-20000000000
χ14222222222222-2-2-2-2-2-2-2-2-222-2200000000000000000000-2-2220000000000
χ1522222222-2-2-2-22222-2-222-222-2-2000000000000000000000000000000002-2
χ1622222222-2-2-2-22222-2-222-222-2-200000000000000000000000000000000-22
χ1722222222-2-2-2-22222-2-2-2-22-2-22200000000000000000000000022-2-2000000
χ1822222222-2-2-2-22222-2-2-2-22-2-222000000000000000000000000-2-222000000
χ1922222222-2-2-2-2-2-2-2-22222-2-2-2-2200000000000000000000000000002i2i−2i−2i00
χ2022222222-2-2-2-2-2-2-2-22222-2-2-2-220000000000000000000000000000−2i−2i2i2i00
χ2122222222-2-2-2-2-2-2-2-222-2-22222-2000000002222-2-2-2-2000000000000000000
χ2222222222-2-2-2-2-2-2-2-222-2-22222-200000000-2-2-2-22222000000000000000000
χ232222-2-2-2-222-2-222-2-22-200000000000000022−2−222−2−22-200000000002−22−200
χ242222-2-2-2-222-2-222-2-22-200000000000000022−2−222−2−2-220000000000−22−2200
χ252222-2-2-2-222-2-222-2-22-2000000000000000−2−222−2−2222-20000000000−22−2200
χ262222-2-2-2-222-2-222-2-22-2000000000000000−2−222−2−222-2200000000002−22−200
χ272222-2-2-2-2-2-222-2-2222-200000000000000022−2−2−2−222002i−2i00000000i2−i2−i2i200
χ282222-2-2-2-2-2-222-2-2222-200000000000000022−2−2−2−22200−2i2i00000000−i2i2i2−i200
χ292222-2-2-2-2-2-222-2-2222-2000000000000000−2−22222−2−2002i−2i00000000−i2i2i2−i200
χ302222-2-2-2-2-2-222-2-2222-2000000000000000−2−22222−2−200−2i2i00000000i2−i2−i2i200
χ3122-2-222-2-22-22-20000002-2-20020000022-2-2i2−i2i2−i2i2−i2i2−i200000000i2−i2i2−i2000000
χ3222-2-222-2-22-22-20000002-2-20020000022-2-2−i2i2−i2i2−i2i2−i2i200000000−i2i2−i2i2000000
χ3322-2-222-2-22-22-20000002-2-200200000-2-222i2−i2i2−i2i2−i2i2−i200000000−i2i2−i2i2000000
χ3422-2-222-2-22-22-20000002-2-200200000-2-222−i2i2−i2i2−i2i2−i2i200000000i2−i2i2−i2000000
χ3522-2-222-2-2-22-22000000-22-2002022-2-20000i2−i2i2−i2−i2i2−i2i200000000i2−i2−i2i2000000
χ3622-2-222-2-2-22-22000000-22-2002022-2-20000−i2i2−i2i2i2−i2i2−i200000000−i2i2i2−i2000000
χ3722-2-222-2-2-22-22000000-22-20020-2-2220000i2−i2i2−i2−i2i2−i2i200000000−i2i2i2−i2000000
χ3822-2-222-2-2-22-22000000-22-20020-2-2220000−i2i2−i2i2i2−i2i2−i200000000i2−i2−i2i2000000
χ394444-4-4-4-444-4-4-4-444-4400000000000000000000000000000000000000000
χ404444-4-4-4-4-4-44444-4-4-4400000000000000000000000000000000000000000
χ4144-4-444-4-44-44-4000000-44400-400000000000000000000000000000000000
χ4244-4-444-4-4-44-440000004-4400-400000000000000000000000000000000000
χ4344-4-4-4-4444-4-440000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ4444-4-4-4-4444-4-44000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ4544-4-4-4-444-444-40000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ4644-4-4-4-444-444-4000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ474-44-44-4-4400004-44-40000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ484-44-44-4-4400004-44-4000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ494-44-44-4-440000-44-440000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ504-44-44-4-440000-44-44000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ514-44-4-444-400004-4-44000000000000000000000000000002i−2i2i−2i0000000000
χ524-44-4-444-400004-4-4400000000000000000000000000000−2i2i−2i2i0000000000
χ534-44-4-444-40000-444-4000000000000000000000000000002i−2i−2i2i0000000000
χ544-44-4-444-40000-444-400000000000000000000000000000−2i2i2i−2i0000000000
χ554-4-444-44-400000000000004-4002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ564-4-444-44-400000000000004-400−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ574-4-444-44-40000000000000-44002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ584-4-444-44-40000000000000-4400−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ598-8-88-88-88000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).