Finite Group Databasebeta

← Group #146166

Character table — Group #146166

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222222244444448888888888888888816161616161616161616161632323232
order12222244444488884448888444488888161616161616161688888888161616164488
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ511111111111111111111111-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ811111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ9222222222222-2-2-2-2222-2-2-2-22222-2-2-2-2-2000000000000000000000000
χ10222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ11222222222-2-222222-2-2-222-2-20000-200002222-2-2-2-20000000000000000
χ12222222222-2-222222-2-2-222-2-20000-20000-2-2-2-222220000000000000000
χ13222222222-2-22-2-2-2-2-2-2-2-2-22200002000000000000000000002i2i−2i−2i0000
χ14222222222-2-22-2-2-2-2-2-2-2-2-2220000200000000000000000000−2i−2i2i2i0000
χ152222-2-22-2-222200002-2-200000000022-2-2i2i2−i2−i2i2i2−i2−i200000000i2−i2i2−i20000
χ162222-2-22-2-222200002-2-200000000022-2-2−i2−i2i2i2−i2−i2i2i200000000−i2i2−i2i20000
χ172222-2-22-2-222200002-2-2000000000-2-222i2i2−i2−i2i2i2−i2−i200000000−i2i2−i2i20000
χ182222-2-22-2-222200002-2-2000000000-2-222−i2−i2i2i2−i2−i2i2i200000000i2−i2i2−i20000
χ192222-2-22-2-2-2-220000-22200002i2i−2i−2i00000i2i2−i2−i2−i2−i2i2i2000000002−2−220000
χ202222-2-22-2-2-2-220000-22200002i2i−2i−2i00000−i2−i2i2i2i2i2−i2−i200000000−222−20000
χ212222-2-22-2-2-2-220000-2220000−2i−2i2i2i00000i2i2−i2−i2−i2−i2i2i200000000−222−20000
χ222222-2-22-2-2-2-220000-2220000−2i−2i2i2i00000−i2−i2i2i2i2i2−i2−i2000000002−2−220000
χ232222-2-2-22222-22222-22-2-2-2220000-2000000000000000000000000002i−2i
χ242222-2-2-22222-22222-22-2-2-2220000-200000000000000000000000000−2i2i
χ252222-2-2-22222-2-2-2-2-2-22-222-2-20000200000000000022-2-2000000000000
χ262222-2-2-22222-2-2-2-2-2-22-222-2-200002000000000000-2-222000000000000
χ272222-2-2-222-2-2-222222-22-2-2-2-2000020000000000000000000000002i−2i00
χ282222-2-2-222-2-2-222222-22-2-2-2-200002000000000000000000000000−2i2i00
χ292222-2-2-222-2-2-2-2-2-2-22-2222220000-2000000000000000022-2-200000000
χ302222-2-2-222-2-2-2-2-2-2-22-2222220000-20000000000000000-2-22200000000
χ3122-2-22-222-200-222-2-20002-2000000000002-22-200002−22−22−22−200000000
χ3222-2-22-222-200-222-2-20002-2000000000002-22-20000−22−22−22−2200000000
χ3322-2-22-222-200-222-2-20002-200000000000-22-2200002−22−2−22−2200000000
χ3422-2-22-222-200-222-2-20002-200000000000-22-220000−22−222−22−200000000
χ3522-2-2-22-22-2002-2-2220002-20000000000000002-22-22−2−222−2−2200000000
χ3622-2-2-22-22-2002-2-2220002-20000000000000002-22-2−222−2−222−200000000
χ3722-2-2-22-22-2002-2-2220002-2000000000000000-22-222−2−22−222−200000000
χ3822-2-2-22-22-2002-2-2220002-2000000000000000-22-22−222−22−2−2200000000
χ39444444-4-4-444-40000-4-440000000000000000000000000000000000000
χ40444444-4-4-4-4-4-4000044-40000000000000000000000000000000000000
χ4144-4-44-444-400-4-4-444000-4400000000000000000000000000000000000
χ4244-4-44-4-4-440040000000000000000000000002i2−2i2−2i22i20000000000000000
χ4344-4-44-4-4-44004000000000000000000000000−2i22i22i2−2i20000000000000000
χ4444-4-4-444-4400-4000000000000000000002i2−2i2−2i22i200000000000000000000
χ4544-4-4-444-4400-400000000000000000000−2i22i22i2−2i200000000000000000000
χ4644-4-4-44-44-400444-4-4000-4400000000000000000000000000000000000
χ474-44-4000004-402i2−2i22i2−2i2000002i2−2i22-22-20002i2−2i2000000000000000000000000
χ484-44-4000004-402i2−2i22i2−2i2000002i2−2i2-22-22000−2i22i2000000000000000000000000
χ494-44-4000004-40−2i22i2−2i22i200000−2i22i22-22-2000−2i22i2000000000000000000000000
χ504-44-4000004-40−2i22i2−2i22i200000−2i22i2-22-220002i2−2i2000000000000000000000000
χ514-44-400000-4402i2−2i22i2−2i200000−2i22i22i−2i−2i2i022−2200000000000000000000000000
χ524-44-400000-4402i2−2i22i2−2i200000−2i22i2−2i2i2i−2i0−222200000000000000000000000000
χ534-44-400000-440−2i22i2−2i22i2000002i2−2i22i−2i−2i2i0−222200000000000000000000000000
χ544-44-400000-440−2i22i2−2i22i2000002i2−2i2−2i2i2i−2i022−2200000000000000000000000000
χ558-8-88000000004i2−4i2−4i24i20000000000000000000000000000000000000000
χ568-8-8800000000−4i24i24i2−4i20000000000000000000000000000000000000000

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