Finite Group Databasebeta

← Group #167905

Character table — Group #167905

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444444444888888882444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-111111111-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ61111111111111111111111-1-1-1-111111111-1-1-111-111-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-11111-1-1-1-1
χ911111111-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-11-111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-11-1-1-11-1-1111-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111111111-1-11-1-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111111-1-1-11-1-11-1-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-111-111-11-1-111-1-111-1-1-1-111
χ1411111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-11-111-1-1-11111-1-11111-1-1
χ1511111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-111-111-1111-1-1-1-1-1-11111-1-1
χ1611111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-11-111-111-1-11111-1-1-1-111
χ1722222222222222-22-2-2-22-2-2222200000000-20000-20000000000000000
χ1822222222222222-22-2-2-22-2-2-2-2-2-2000000002000020000000000000000
χ19222222222222-2-22-2-2-22-22-200000000000002-20000000002-200000000
χ20222222222222-2-22-2-2-22-22-20000000000000-22000000000-2200000000
χ21222222222222-2-2-2-222-2-2-220000000000000002-20-2200000000000000
χ22222222222222-2-2-2-222-2-2-22000000000000000-2202-200000000000000
χ2322222222-2-2-2-2222-2-2-22-2-2200000000000002-2000000000-2200000000
χ2422222222-2-2-2-2222-2-2-22-2-220000000000000-220000000002-200000000
χ2522222222-2-2-2-222-2-222-2-22-2000000000000000220-2-200000000000000
χ2622222222-2-2-2-222-2-222-2-22-2000000000000000-2-202200000000000000
χ2722222222-2-2-2-2-2-2-22-2-2-222222-2-200000000-2000020000000000000000
χ2822222222-2-2-2-2-2-2-22-2-2-2222-2-2220000000020000-20000000000000000
χ2922-2-222-2-222-2-22-20-20002002i−2i2i−2i0000000000000000000000i2−i2i2−i22−22−2
χ3022-2-222-2-222-2-22-20-20002002i−2i2i−2i0000000000000000000000−i2i2−i2i2−22−22
χ3122-2-222-2-222-2-22-20-2000200−2i2i−2i2i0000000000000000000000i2−i2i2−i2−22−22
χ3222-2-222-2-222-2-22-20-2000200−2i2i−2i2i0000000000000000000000−i2i2−i2i22−22−2
χ3322-2-222-2-2-2-222-220-20002002i−2i−2i2i0000000000000000000000i2−i2−i2i22−2−22
χ3422-2-222-2-2-2-222-220-20002002i−2i−2i2i0000000000000000000000−i2i2i2−i2−222−2
χ3522-2-222-2-2-2-222-220-2000200−2i2i2i−2i0000000000000000000000i2−i2−i2i2−222−2
χ3622-2-222-2-2-2-222-220-2000200−2i2i2i−2i0000000000000000000000−i2i2i2−i22−2−22
χ37444-4-4-44-40000004000-4000000000002222−22−220000000000000000000000
χ38444-4-4-44-40000004000-400000000000−22−2222220000000000000000000000
χ39444-4-4-44-4000000-4000400000002i22i2−2i2−2i200000000000000000000000000
χ40444-4-4-44-4000000-400040000000−2i2−2i22i22i200000000000000000000000000
χ4144-4-444-4-444-4-4-4404000-4000000000000000000000000000000000000
χ4244-4-444-4-4-4-4444-404000-4000000000000000000000000000000000000
χ434-44-44-4-444i−4i4i−4i0000000000000000000000000000002-22i−2i0000000000
χ444-44-44-4-444i−4i4i−4i000000000000000000000000000000-22−2i2i0000000000
χ454-44-44-4-44−4i4i−4i4i0000000000000000000000000000002-2−2i2i0000000000
χ464-44-44-4-44−4i4i−4i4i000000000000000000000000000000-222i−2i0000000000
χ474-4-444-44-44i−4i−4i4i000000000000002i−2i2i−2i2-22-20000000000000000000000
χ484-4-444-44-44i−4i−4i4i00000000000000−2i2i−2i2i-22-220000000000000000000000
χ494-4-444-44-4−4i4i4i−4i000000000000002i−2i2i−2i-22-220000000000000000000000
χ504-4-444-44-4−4i4i4i−4i00000000000000−2i2i−2i2i2-22-20000000000000000000000
χ514-4-4-4-4444000000004-400000000000022−22−22220000000000000000000000
χ524-4-4-4-4444000000004-4000000000000−222222−220000000000000000000000
χ534-4-4-4-444400000000-440000000022−22−222200000000000000000000000000
χ544-4-4-4-444400000000-4400000000−222222−2200000000000000000000000000
χ5588-88-8-8-88000000000000000000000000000000000000000000000000
χ568-888-88-8-8000000000000000000000000000000000000000000000000

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