Finite Group Databasebeta

← Group #340340

Character table — Group #340340

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488882244444488888888888888444444888888244
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111111111111111111-1-1-1-1-111-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1111111-1-11111-1-1-1-1-1-1-111-1-11-1-1-1-1-1-111-1
χ4111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-111-1-1-11111-1-11
χ51111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11
χ61111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111111111-1
χ71111111111111111111111-1-1-1-111-1-11111-1-1-1-1111111-111-1-11-1-11111-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-111-111-1-1-111-1-11-1-1
χ10111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-111-1-1-1-11-11-1-11-1-1-1-111-111
χ11111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-111-1-1111-11
χ12111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-11-1
χ13111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111111-111-1-1-1-1-111-11-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111-11-1-11-1-111-1-11-11
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11-1-1-1-11111-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1111-1-1
χ172222222222-2-22-22-2-2-20000222200-2-200-2-20000220000-200000000000000
χ182222222222-2-22-22-2-2-2000022-2-200-2-200220000-2-20000200000000000000
χ192222222222-2-22-22-2-2-20000-2-222002200220000-2-20000-200000000000000
χ202222222222-2-22-22-2-2-20000-2-2-2-2002200-2-20000220000200000000000000
χ2122222222-2-222-22-22-2-2222200002200-2-20000000000000-2-2002000000000
χ2222222222-2-222-22-22-2-222220000-2-200-2-200000000000002200-2000000000
χ2322222222-2-222-22-22-2-2-2-2-2-200002200220000000000000-2200-2000000000
χ2422222222-2-222-22-22-2-2-2-2-2-20000-2-2002200000000000002-2002000000000
χ25222-22-2-2-22-200-20200022−2−2002-2002i−2i2−22i−2ii2i2−i2−i200i2i2−i2−i20000002−20000000
χ26222-22-2-2-22-200-20200022−2−2002-200−2i2i2−2−2i2i−i2−i2i2i200−i2−i2i2i20000002−20000000
χ27222-22-2-2-22-200-20200022−2−200-22002i−2i2−2−2i2ii2i2−i2−i200−i2−i2i2i2000000−220000000
χ28222-22-2-2-22-200-20200022−2−200-2200−2i2i2−22i−2i−i2−i2i2i200i2i2−i2−i2000000−220000000
χ29222-22-2-2-22-200-202000−2−222002-2002i−2i−222i−2i−i2−i2i2i200−i2−i2i2i2000000−220000000
χ30222-22-2-2-22-200-202000−2−222002-200−2i2i−22−2i2ii2i2−i2−i200i2i2−i2−i2000000−220000000
χ31222-22-2-2-22-200-202000−2−22200-22002i−2i−22−2i2i−i2−i2i2i200i2i2−i2−i20000002−20000000
χ32222-22-2-2-22-200-202000−2−22200-2200−2i2i−222i−2ii2i2−i2−i200−i2−i2i2i20000002−20000000
χ3322-2-2-2-222-2-2-2-222222-200000000000000002-22-20000000002-2000002-2000
χ3422-2-2-2-222-2-2-2-222222-200000000000000002-22-2000000000-2200000-22000
χ3522-2-2-2-222-2-2-2-222222-20000000000000000-22-220000000002-200000-22000
χ3622-2-2-2-222-2-2-2-222222-20000000000000000-22-22000000000-22000002-2000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-44-4-4-4-440040-40002222−22−2200000000−2222000000000000000000000000000
χ39444-44-4-4-4-440040-4000−22−2222220000000022−22000000000000000000000000000
χ4044-44-44-4-44-40040-400000004-400000000000000000000000000000000000
χ4144-44-44-4-44-40040-40000000-4400000000000000000000000000000000000
χ4244-44-44-4-4-4400-40400000000000000000002i2−2i2−2i22i2000000000000000000000
χ4344-44-44-4-4-4400-4040000000000000000000−2i22i22i2−2i2000000000000000000000
χ4444-4-4-4-4444444-4-4-4-44-400000000000000000000000000000000000000000
χ4544-4-4-4-44444-4-4-44-44-4400000000000000000000000000000000000000000
χ4644-4-4-4-444-4-4444-44-4-4400000000000000000000000000000000000000000
χ474-444-4-44-400000000002i2−2i22i2−2i2000000000000000022−222i−2i2i−2i000000000000000
χ484-444-4-44-400000000002i2−2i22i2−2i20000000000000000−2222−2i2i−2i2i000000000000000
χ494-444-4-44-40000000000−2i22i2−2i22i2000000000000000022−22−2i2i−2i2i000000000000000
χ504-444-4-44-40000000000−2i22i2−2i22i20000000000000000−22222i−2i2i−2i000000000000000
χ514-44-4-44-44004-4040-4004i−4i−4i4i0000000000000000000000000000000000000
χ524-44-4-44-44004-4040-400−4i4i4i−4i0000000000000000000000000000000000000
χ534-44-4-44-4400-440-40400000000000000000000000022−22−2222000000000000000
χ544-44-4-44-4400-440-404000000000000000000000000−222222−22000000000000000
χ554-4-444-4-44004-40-40400000000004-40000000000000000000000000000000
χ564-4-444-4-44004-40-4040000000000-440000000000000000000000000000000
χ574-4-444-4-4400-44040-40000000000000000000000000000000000002i2−2i200000
χ584-4-444-4-4400-44040-4000000000000000000000000000000000000−2i22i200000
χ598-8-8-8888-8000000000000000000000000000000000000000000000000000

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