Finite Group Databasebeta

← Group #337005

Character table — Group #337005

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488884444444488888888888888244444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-111
χ3111111111111111111111111-1-11111111111111111111-1-1-1-1-111-1-1-1-1-1-1-1
χ4111111111111111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-111-1-1-111111-1-1
χ51111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1
χ61111111111111111111111-1-111-1-1-1-11111-1-1-1-1111111-111-1-11-1-11111-1-1-1
χ71111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1111111-111
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11-1111-1-1-111-1-1-11-1
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-111-1-11111-1
χ11111111111111111111-1-1-1-111-1-11111-1-111-1-1-1-111-1-1-1-111-1-1-11-1-1-1-1111-11
χ12111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11111111-1-1-1-11
χ13111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-111111-1111-1-1-1-1-111-1-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-11111-1-11-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-11-1-111-1-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-111111-1-111-11-1
χ172222222222-22-2-2-22-2-200002200-2-22200-2-20000220000-200000000000000
χ182222222222-22-2-2-22-2-200002200-2-2-2-200220000-2-20000200000000000000
χ192222222222-22-2-2-22-2-20000-2-200222200220000-2-20000-200000000000000
χ202222222222-22-2-2-22-2-20000-2-20022-2-200-2-20000220000200000000000000
χ2122222222-2-22-2222-2-2-2222200220000-2-200000000000002-200-2000000000
χ2222222222-2-22-2222-2-2-2222200-2-20000-2-20000000000000-22002000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-200220000220000000000000-2-2002000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-200-2-200002200000000000002200-2000000000
χ25222-2-2-2-22-2-2-2222-222-200000000000000002i2i−2i−2i0000000002i−2i000002-2000
χ26222-2-2-2-22-2-2-2222-222-200000000000000002i2i−2i−2i000000000−2i2i00000-22000
χ27222-2-2-2-22-2-2-2222-222-20000000000000000−2i−2i2i2i0000000002i−2i00000-22000
χ28222-2-2-2-22-2-2-2222-222-20000000000000000−2i−2i2i2i000000000−2i2i000002-2000
χ2922-22-22-2-22-20-200020022−2−200002-22i−2i2−22i−2i2−22−200i2i2−i2−i2000000i2−i20000000
χ3022-22-22-2-22-20-200020022−2−200002-2−2i2i2−2−2i2i2−22−200−i2−i2i2i2000000−i2i20000000
χ3122-22-22-2-22-20-200020022−2−20000-222i−2i2−2−2i2i−22−2200−i2−i2i2i2000000i2−i20000000
χ3222-22-22-2-22-20-200020022−2−20000-22−2i2i2−22i−2i−22−2200i2i2−i2−i2000000−i2i20000000
χ3322-22-22-2-22-20-2000200−2−22200002-22i−2i−222i−2i−22−2200−i2−i2i2i2000000−i2i20000000
χ3422-22-22-2-22-20-2000200−2−22200002-2−2i2i−22−2i2i−22−2200i2i2−i2−i2000000i2−i20000000
χ3522-22-22-2-22-20-2000200−2−2220000-222i−2i−22−2i2i2−22−200i2i2−i2−i2000000−i2i20000000
χ3622-22-22-2-22-20-2000200−2−2220000-22−2i2i−222i−2i2−22−200−i2−i2i2i2000000i2−i20000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-4-4-4-44444-4-4-44-44-400000000000000000000000000000000000000000
χ39444-4-4-4-4444-4-444-4-4-4400000000000000000000000000000000000000000
χ40444-4-4-4-44-4-444-4-444-4400000000000000000000000000000000000000000
χ4144-44-44-4-4-4404000-4002222−22−2200000000−2222000000000000000000000000000
χ4244-44-44-4-4-4404000-400−22−2222220000000022−22000000000000000000000000000
χ4344-4-44-44-44-404000-40000004-400000000000000000000000000000000000
χ4444-4-44-44-44-404000-4000000-4400000000000000000000000000000000000
χ4544-4-44-44-4-440-400040000000000000000002i2−2i2−2i22i2000000000000000000000
χ4644-4-44-44-4-440-40004000000000000000000−2i22i22i2−2i2000000000000000000000
χ474-44-4-444-400000000002i2−2i22i2−2i2000000000000000022−222i−2i2i−2i000000000000000
χ484-44-4-444-400000000002i2−2i22i2−2i20000000000000000−2222−2i2i−2i2i000000000000000
χ494-44-4-444-40000000000−2i22i2−2i22i2000000000000000022−22−2i2i−2i2i000000000000000
χ504-44-4-444-40000000000−2i22i2−2i22i20000000000000000−22222i−2i2i−2i000000000000000
χ514-4-44-4-44400404-4-40000000004i−4i000000000000000000000000000000000
χ524-4-44-4-44400404-4-4000000000−4i4i000000000000000000000000000000000
χ534-4-44-4-44400-40-444000000000000000000000000000000000000022−2200000
χ544-4-44-4-44400-40-4440000000000000000000000000000000000000−222200000
χ554-4-4-444-440040-44-40004i−4i−4i4i0000000000000000000000000000000000000
χ564-4-4-444-440040-44-4000−4i4i4i−4i0000000000000000000000000000000000000
χ574-4-4-444-4400-404-44000000000000000000000000022−22−2222000000000000000
χ584-4-4-444-4400-404-440000000000000000000000000−222222−22000000000000000
χ598-8888-8-8-8000000000000000000000000000000000000000000000000000

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