Finite Group Databasebeta

← Group #166802

Character table — Group #166802

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444422444444442244444448888888824444444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1111-1-111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1111111-1-1-1-1
χ51111111111111111111111-1-1111-1-11111111111-1-1-1-11-1111-111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-11-1-1-1-1111111111-11-1-11-1-1-11-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11-111111-1-1-1-11111
χ911111111-1-1-1-1-1-111-1-111111111-1-1-1-1-11111-1-1-1-11-1-11-11111-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-111111-1-11-111-1-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-1111-1-11111-1-1
χ1211111111-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1-1-1-11111-1-1111-1-1111-1-111-1-1-1-111
χ1311111111-1-1-1-1-1-111-1-11111-1-111-111-1-11111-1-1-1-1-111-1-1-11111-1-1-1-111-1-111
χ1411111111-1-1-1-1-1-111-1-11111-1-111-111-1-1-1-1-1-11111-111-1-1-11-1-111111-1-111-1-1
χ1511111111-1-1-1-1-1-111-1-11111-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-1-1-111-1-11111-1-1-1-1-11111-1-1-1-1111111-1-111-111-1-1-1-1-11111-1-1
χ17222222222222222-2-2-2-2-22-20022-200-2-200000000000020-20000000000000
χ18222222222222222-2-2-2-2-22-200-2-2-20022000000000000-2020000000000000
χ19222222222222-2-2-22-2-2-2-2-220000200000000000020-200-200020000000000
χ20222222222222-2-2-22-2-2-2-2-2200002000000000000-202002000-20000000000
χ21222222222222-2-2-2-22222-2-22200-22200000000000-20-20000000000000000
χ22222222222222-2-2-2-22222-2-2-2-200-2-2-2000000000002020000000000000000
χ2322222222-2-2-2-222-2222-2-2-220000-200000000000020200-2000-20000000000
χ2422222222-2-2-2-222-2222-2-2-220000-2000000000000-20-200200020000000000
χ2522222222-2-2-2-222-2-2-2-222-2-222002-2-20000000000020-20000000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-2-2-20022200000000000-2020000000000000000
χ2722222222-2-2-2-2-2-22-222-2-22-2002220022000000000000-20-20000000000000
χ2822222222-2-2-2-2-2-22-222-2-22-200-2-2200-2-20000000000002020000000000000
χ2922-2-22-22-22i2i−2i−2i00002i−2i2-2002-20002i−2i0022−2−2i2i2−i2−i200000000000000002−2i2−i2
χ3022-2-22-22-22i2i−2i−2i00002i−2i2-2002-20002i−2i00−2−222−i2−i2i2i20000000000000000−22−i2i2
χ3122-2-22-22-22i2i−2i−2i00002i−2i2-200-22000−2i2i0022−2−2i2i2−i2−i20000000000000000−22−i2i2
χ3222-2-22-22-22i2i−2i−2i00002i−2i2-200-22000−2i2i00−2−222−i2−i2i2i200000000000000002−2i2−i2
χ3322-2-22-22-2−2i−2i2i2i0000−2i2i2-2002-2000−2i2i0022−2−2−i2−i2i2i200000000000000002−2−i2i2
χ3422-2-22-22-2−2i−2i2i2i0000−2i2i2-2002-2000−2i2i00−2−222i2i2−i2−i20000000000000000−22i2−i2
χ3522-2-22-22-2−2i−2i2i2i0000−2i2i2-200-220002i−2i0022−2−2−i2−i2i2i20000000000000000−22i2−i2
χ3622-2-22-22-2−2i−2i2i2i0000−2i2i2-200-220002i−2i00−2−222i2i2−i2−i200000000000000002−2−i2i2
χ374444-4-4-4-400004-4000000000000000002-22-22-22-200000000000000000000
χ384444-4-4-4-400004-400000000000000000-22-22-22-2200000000000000000000
χ394444-4-4-4-40000-44000000000000000002-22-2-22-2200000000000000000000
χ404444-4-4-4-40000-4400000000000000000-22-222-22-200000000000000000000
χ4144-4-44-44-44i4i−4i−4i0000−4i4i-44000000000000000000000000000000000000000
χ4244-4-44-44-4−4i−4i4i4i00004i−4i-44000000000000000000000000000000000000000
χ4344-4-4-44-440000000400000-400000000000002i2−2i2−2i22i200000000000000000000
χ4444-4-4-44-440000000400000-40000000000000−2i22i22i2−2i200000000000000000000
χ4544-4-4-44-440000000-400000400000000022−22−2222000000000000000000000000
χ4644-4-4-44-440000000-4000004000000000−222222−22000000000000000000000000
χ474-44-444-4-4000000400000-40004-4000000000000000000000000000000000
χ484-44-444-4-4000000400000-4000-44000000000000000000000000000000000
χ494-44-444-4-4000000-4000004000000004i−4i0000000000000000000000000000
χ504-44-444-4-4000000-400000400000000−4i4i0000000000000000000000000000
χ514-44-4-4-4444-44-400000000000000000000000000000000002-202-200000000
χ524-44-4-4-4444-44-40000000000000000000000000000000000-220-2200000000
χ534-44-4-4-444-44-4400000000000000000000000000000000002-20-2200000000
χ544-44-4-4-444-44-440000000000000000000000000000000000-2202-200000000
χ554-4-44-444-44i−4i−4i4i0000000000000000000000000000000000000002-22i−2i0000
χ564-4-44-444-44i−4i−4i4i000000000000000000000000000000000000000-22−2i2i0000
χ574-4-44-444-4−4i4i4i−4i0000000000000000000000000000000000000002-2−2i2i0000
χ584-4-44-444-4−4i4i4i−4i000000000000000000000000000000000000000-222i−2i0000
χ598-8-888-8-88000000000000000000000000000000000000000000000000000

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