Finite Group Databasebeta

← Group #288136

Character table — Group #288136

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888882244444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111111111-1-1-1-111-1-111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1111-111-1-1-1-111-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-111-1-111-11
χ71111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-111-11
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1111111-1-11-1
χ911111111111111111-1-1-1-111111-1-1111111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1
χ1011111111111111111-1-1-1-111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-11-1-1-1111111-1-1-11
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11-11111-1-1-1-1111-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-11-1-1-1-111-1-1111-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1111-1-1-1-111-1-1-11
χ172222222222-22-2-2-22-22222-20000-2-2000022000000-2-2000000002-20000000000
χ182222222222-22-2-2-22-22222-20000-2-20000-2-20000002200000000-220000000000
χ192222222222-22-2-2-22-2-2-2-2-2-2000022000022000000-2-200000000-220000000000
χ202222222222-22-2-2-22-2-2-2-2-2-20000220000-2-200000022000000002-20000000000
χ2122222222-2-22-2222-2-20000-22222002222000000-2-200000000-2-2000000000000
χ2222222222-2-22-2222-2-20000-2222200-2-2-2-2000000-2-20000000022000000000000
χ2322222222-2-22-2222-2-20000-2-2-2-2-20022-2-20000002200000000-22000000000000
χ2422222222-2-22-2222-2-20000-2-2-2-2-200-2-22200000022000000002-2000000000000
χ25222-2-2-2-2200202-2-2000000022-2-2002i−2i2i−2i2−20000002−222−2−20000000000i2−i2i2−i200
χ26222-2-2-2-2200202-2-2000000022-2-2002i−2i2i−2i−22000000−22−2−2220000000000−i2i2−i2i200
χ27222-2-2-2-2200202-2-2000000022-2-200−2i2i−2i2i2−20000002−222−2−20000000000−i2i2−i2i200
χ28222-2-2-2-2200202-2-2000000022-2-200−2i2i−2i2i−22000000−22−2−2220000000000i2−i2i2−i200
χ29222-2-2-2-2200202-2-20000000-2-222002i−2i−2i2i2−20000002−2−2−2220000000000i2−i2−i2i200
χ30222-2-2-2-2200202-2-20000000-2-222002i−2i−2i2i−22000000−2222−2−20000000000−i2i2i2−i200
χ31222-2-2-2-2200202-2-20000000-2-22200−2i2i2i−2i2−20000002−2−2−2220000000000−i2i2i2−i200
χ32222-2-2-2-2200202-2-20000000-2-22200−2i2i2i−2i−22000000−2222−2−20000000000i2−i2−i2i200
χ332-2-222-2-22222-2-22-2-2-22i2i−2i−2i200002i−2i000000000000002-22-2000000002i−2i000000
χ342-2-222-2-22222-2-22-2-2-22i2i−2i−2i200002i−2i00000000000000-22-2200000000−2i2i000000
χ352-2-222-2-22222-2-22-2-2-2−2i−2i2i2i20000−2i2i000000000000002-22-200000000−2i2i000000
χ362-2-222-2-22222-2-22-2-2-2−2i−2i2i2i20000−2i2i00000000000000-22-22000000002i−2i000000
χ372-2-222-2-2222-2-22-22-222i2i−2i−2i-22-22-2−2i2i0000002i2i−2i−2i2-20000000000000000000000
χ382-2-222-2-2222-2-22-22-222i2i−2i−2i-2-22-22−2i2i000000−2i−2i2i2i-220000000000000000000000
χ392-2-222-2-2222-2-22-22-22−2i−2i2i2i-22-22-22i−2i000000−2i−2i2i2i2-20000000000000000000000
χ402-2-222-2-2222-2-22-22-22−2i−2i2i2i-2-22-222i−2i0000002i2i−2i−2i-220000000000000000000000
χ412-2-222-2-22-2-2-222-222-2000022-22-2000000000000-220000002-200002-200000000
χ422-2-222-2-22-2-2-222-222-2000022-22-2000000000000-22000000-220000-2200000000
χ432-2-222-2-22-2-2-222-222-200002-22-220000000000002-20000002-20000-2200000000
χ442-2-222-2-22-2-2-222-222-200002-22-220000000000002-2000000-2200002-200000000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ46444-4-4-4-4400-40-4440000000000000000022−22000000−222200000000000000000000
χ47444-4-4-4-4400-40-44400000000000000000−222200000022−2200000000000000000000
χ4844-44-44-4-44-404000-400000000000000000022−2222−22000000000000000000000000
χ4944-44-44-4-44-404000-4000000000000000000−2222−2222000000000000000000000000
χ5044-44-44-4-4-440-4000404i−4i4i−4i00000000000000000000000000000000000000000
χ5144-44-44-4-4-440-400040−4i4i−4i4i00000000000000000000000000000000000000000
χ524-444-4-44-44-40-400040000000000000000002i2−2i2−2i22i2000000000000000000000000
χ534-444-4-44-44-40-40004000000000000000000−2i22i22i2−2i2000000000000000000000000
χ544-444-4-44-4-4404000-404-4-4400000000000000000000000000000000000000000
χ554-444-4-44-4-4404000-40-444-400000000000000000000000000000000000000000
χ564-4-444-4-44-4-444-44-4440000-40000000000000000000000000000000000000000
χ574-4-4-4-44440040-4-4400000000000000000000000000022−22−22220000000000000000
χ584-4-4-4-44440040-4-44000000000000000000000000000−222222−220000000000000000
χ594-4-4-4-444400-4044-400000004-4-44000000000000000000000000000000000000
χ604-4-4-4-444400-4044-40000000-444-4000000000000000000000000000000000000
χ6188-8-88-88-8000000000000000000000000000000000000000000000000000000
χ628-88-888-8-8000000000000000000000000000000000000000000000000000000

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