Finite Group Databasebeta

← Group #168896

Character table — Group #168896

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444444444444444444888888882444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1111-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1
χ4111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ51111111111111111111111-1-1111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ71111111111111111111111-1-1-1-11-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1
χ911111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-111-1-11111-1-1-1-1-111-11-111-1-111-1-11-1
χ1011111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-111-1-1-1-1-1-11111-111-11-1-1-111-1-111-11
χ1111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-111-1-1111111-1-1-1-11-11-1-1111-1-1-1-111-11
χ1211111111-1-1-1-11-1-1-1-11111111-1-1-1-1-111-1-111-1-1-1-111111-11-1-11-1-11111-1-11-1
χ1311111111-1-1-1-11-1-1-1-111111-1-111-111-1-1-1-1111111-1-1-1-11-1-111-1-1-11111-1-1-11
χ1411111111-1-1-1-11-1-1-1-111111-1-111-111-1-1-1-111-1-1-1-111111-1-111-111-1-1-1-1111-1
χ1511111111-1-1-1-11-1-1-1-111111-1-1-1-1-1111111-1-11111-1-1-1-1-11-11-11-1-111-1-1111-1
χ1611111111-1-1-1-11-1-1-1-111111-1-1-1-1-1111111-1-1-1-1-1-11111-11-11-1111-1-111-1-1-11
χ172222222222222-2-2-2-2-2-2-2-22000020000222200000000-2-200000000000000
χ182222222222222-2-2-2-2-2-2-2-22000020000-2-2-2-2000000002200000000000000
χ19222222222222-222-2-222-2-2-20022-200220000000000000000-2-20000000000
χ20222222222222-222-2-222-2-2-200-2-2-200-2-20000000000000000220000000000
χ21222222222222-2-2-222-2-222-22200-2220000000000000000-2-2000000000000
χ22222222222222-2-2-222-2-222-2-2-200-2-2-2000000000000000022000000000000
χ2322222222-2-2-2-222222-2-2-2-220000-2000022-2-2000000002-200000000000000
χ2422222222-2-2-2-222222-2-2-2-220000-20000-2-22200000000-2200000000000000
χ2522222222-2-2-2-2-222-2-2-2-222-222002-2-20000000000000000-22000000000000
χ2622222222-2-2-2-2-222-2-2-2-222-2-2-20022200000000000000002-2000000000000
χ2722222222-2-2-2-2-2-2-22222-2-2-20022200-2-20000000000000000-220000000000
χ2822222222-2-2-2-2-2-2-22222-2-2-200-2-22002200000000000000002-20000000000
χ2922-2-222-2-22i2i−2i−2i0002i−2i002-202i−2i0002-2000000i2i2−i2−i222−2−20000002−2i2−i2000000
χ3022-2-222-2-22i2i−2i−2i0002i−2i002-202i−2i0002-2000000−i2−i2i2i2−2−222000000−22−i2i2000000
χ3122-2-222-2-22i2i−2i−2i0002i−2i002-20−2i2i000-22000000i2i2−i2−i222−2−2000000−22−i2i2000000
χ3222-2-222-2-22i2i−2i−2i0002i−2i002-20−2i2i000-22000000−i2−i2i2i2−2−2220000002−2i2−i2000000
χ3322-2-222-2-2−2i−2i2i2i000−2i2i002-202i−2i000-22000000i2i2−i2−i2−2−2220000002−2−i2i2000000
χ3422-2-222-2-2−2i−2i2i2i000−2i2i002-202i−2i000-22000000−i2−i2i2i222−2−2000000−22i2−i2000000
χ3522-2-222-2-2−2i−2i2i2i000−2i2i002-20−2i2i0002-2000000i2i2−i2−i2−2−222000000−22i2−i2000000
χ3622-2-222-2-2−2i−2i2i2i000−2i2i002-20−2i2i0002-2000000−i2−i2i2i222−2−20000002−2−i2i2000000
χ372-22-22-22-22i−2i2i−2i02i−2i002-2000002i−2i0002-200002−22−2i2−i2i2−i20000000000i2−i22−200
χ382-22-22-22-22i−2i2i−2i02i−2i002-2000002i−2i0002-20000−22−22−i2i2−i2i20000000000−i2i2−2200
χ392-22-22-22-22i−2i2i−2i02i−2i002-200000−2i2i000-2200002−22−2i2−i2i2−i20000000000−i2i2−2200
χ402-22-22-22-22i−2i2i−2i02i−2i002-200000−2i2i000-220000−22−22−i2i2−i2i20000000000i2−i22−200
χ412-22-22-22-2−2i2i−2i2i0−2i2i002-2000002i−2i000-2200002−22−2−i2i2−i2i20000000000i2−i2−2200
χ422-22-22-22-2−2i2i−2i2i0−2i2i002-2000002i−2i000-220000−22−22i2−i2i2−i20000000000−i2i22−200
χ432-22-22-22-2−2i2i−2i2i0−2i2i002-200000−2i2i0002-200002−22−2−i2i2−i2i20000000000−i2i22−200
χ442-22-22-22-2−2i2i−2i2i0−2i2i002-200000−2i2i0002-20000−22−22i2−i2i2−i20000000000i2−i2−2200
χ4544-4-444-4-44i4i−4i−4i000−4i4i00-4400000000000000000000000000000000000000
χ4644-4-444-4-4−4i−4i4i4i0004i−4i00-4400000000000000000000000000000000000000
χ474-44-44-44-44i−4i4i−4i0−4i4i00-440000000000000000000000000000000000000000
χ484-44-44-44-4−4i4i−4i4i04i−4i00-440000000000000000000000000000000000000000
χ494-4-444-4-444-4-44000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ504-4-444-4-444-4-4400000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ514-4-444-4-44-444-4000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ524-4-444-4-44-444-400000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ534-4-4-4-44440000400000000-4000000000004i−4i000000000000000000000000
χ544-4-4-4-44440000400000000-400000000000−4i4i000000000000000000000000
χ554-4-4-4-44440000-40000000040000000004-400000000000000000000000000
χ564-4-4-4-44440000-4000000004000000000-4400000000000000000000000000
χ57888-8-8-8-88000000000000000000000000000000000000000000000000000
χ5888-88-8-88-8000000000000000000000000000000000000000000000000000
χ598-888-88-8-8000000000000000000000000000000000000000000000000000

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