Finite Group Databasebeta

← Group #168735

Character table — Group #168735

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444422444444444444444444444888888884444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ51111111111111111111111-1-11111-1-11-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1
χ911111111-1-1-1-1-1-111-1-111111111-1-1-1-1-111-1-11111-1-1-1-11-11-11-111-1-111-1-11-1
χ1011111111-1-1-1-1-1-111-1-111111111-1-1-1-1-111-1-1-1-1-1-111111-11-11-1-1-111-1-111-11
χ1111111111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1111111-1-1-1-1-111-1-1111-1-1-1-111-11
χ1211111111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-111-1-1-1-11111-111-1-11-1-11111-1-11-1
χ1311111111-1-1-1-1-1-111-1-11111-1-111-1-111-1-1-1111111-1-1-1-1-11-111-1-1-11111-1-1-11
χ1411111111-1-1-1-1-1-111-1-11111-1-111-1-111-1-1-111-1-1-1-11111-11-111-111-1-1-1-1111-1
χ1511111111-1-1-1-1-1-111-1-11111-1-1-1-11111-111-1-11111-1-1-1-11-1-11-11-1-111-1-1111-1
χ1611111111-1-1-1-1-1-111-1-11111-1-1-1-11111-111-1-1-1-1-1-111111-1-11-1111-1-111-1-1-11
χ17222222222222222-2-2-2-2-22-222000022-200000000000000-2-2000000000000
χ18222222222222222-2-2-2-2-22-2-2-20000-2-2-20000000000000022000000000000
χ19222222222222-2-2-22-2-2-2-2-22000000002222200000000-2-200000000000000
χ20222222222222-2-2-22-2-2-2-2-22000000002-2-2-2-2000000002200000000000000
χ21222222222222-2-2-2-22222-2-200222200-20000000000000000-2-20000000000
χ22222222222222-2-2-2-22222-2-200-2-2-2-200-20000000000000000220000000000
χ2322222222-2-2-2-222-2222-2-2-2200000000-222-2-200000000-2200000000000000
χ2422222222-2-2-2-222-2222-2-2-2200000000-2-2-222000000002-200000000000000
χ2522222222-2-2-2-222-2-2-2-222-2-20022-2-20020000000000000000-220000000000
χ2622222222-2-2-2-222-2-2-2-222-2-200-2-22200200000000000000002-20000000000
χ2722222222-2-2-2-2-2-22-222-2-22-2220000-2-2200000000000000-22000000000000
χ2822222222-2-2-2-2-2-22-222-2-22-2-2-20000222000000000000002-2000000000000
χ2922-2-222-2-222-2-22-2-200000202-200002-200000i2i2−i2−i2i2i2−i2−i2000000i2−i2i2−i2000000
χ3022-2-222-2-222-2-22-2-200000202-200002-200000−i2−i2i2i2−i2−i2i2i2000000−i2i2−i2i2000000
χ3122-2-222-2-222-2-22-2-20000020-220000-2200000i2i2−i2−i2i2i2−i2−i2000000−i2i2−i2i2000000
χ3222-2-222-2-222-2-22-2-20000020-220000-2200000−i2−i2i2i2−i2−i2i2i2000000i2−i2i2−i2000000
χ3322-2-222-2-2-2-222-22-200000202-20000-2200000i2i2−i2−i2−i2−i2i2i2000000i2−i2−i2i2000000
χ3422-2-222-2-2-2-222-22-200000202-20000-2200000−i2−i2i2i2i2i2−i2−i2000000−i2i2i2−i2000000
χ3522-2-222-2-2-2-222-22-20000020-2200002-200000i2i2−i2−i2−i2−i2i2i2000000−i2i2i2−i2000000
χ3622-2-222-2-2-2-222-22-20000020-2200002-200000−i2−i2i2i2i2i2−i2−i2000000i2−i2−i2i2000000
χ372-22-22-22-22i−2i2i−2i00002i−2i2-200002-22i−2i0000000i2−i2i2−i22−22−20000000000i2−i22−200
χ382-22-22-22-22i−2i2i−2i00002i−2i2-200002-22i−2i0000000−i2i2−i2i2−22−220000000000−i2i2−2200
χ392-22-22-22-22i−2i2i−2i00002i−2i2-20000-22−2i2i0000000i2−i2i2−i22−22−20000000000−i2i2−2200
χ402-22-22-22-22i−2i2i−2i00002i−2i2-20000-22−2i2i0000000−i2i2−i2i2−22−220000000000i2−i22−200
χ412-22-22-22-2−2i2i−2i2i0000−2i2i2-200002-2−2i2i0000000i2−i2i2−i2−22−220000000000i2−i2−2200
χ422-22-22-22-2−2i2i−2i2i0000−2i2i2-200002-2−2i2i0000000−i2i2−i2i22−22−20000000000−i2i22−200
χ432-22-22-22-2−2i2i−2i2i0000−2i2i2-20000-222i−2i0000000i2−i2i2−i2−22−220000000000−i2i22−200
χ442-22-22-22-2−2i2i−2i2i0000−2i2i2-20000-222i−2i0000000−i2i2−i2i22−22−20000000000i2−i2−2200
χ45444-4-4-4-440000000400000-40000000004-400000000000000000000000000
χ46444-4-4-4-440000000400000-4000000000-4400000000000000000000000000
χ47444-4-4-4-440000000-4000004000000000004i−4i000000000000000000000000
χ48444-4-4-4-440000000-400000400000000000−4i4i000000000000000000000000
χ4944-4-444-4-444-4-4-44400000-400000000000000000000000000000000000000
χ5044-4-444-4-4-4-4444-4400000-400000000000000000000000000000000000000
χ514-44-44-44-44i−4i4i−4i0000−4i4i-44000000000000000000000000000000000000000
χ524-44-44-44-4−4i4i−4i4i00004i−4i-44000000000000000000000000000000000000000
χ534-4-444-4-444i−4i−4i4i000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ544-4-444-4-444i−4i−4i4i00000000000000000000000-222-22i−2i−2i2i0000000000000000
χ554-4-444-4-44−4i4i4i−4i000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ564-4-444-4-44−4i4i4i−4i00000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ5788-88-8-88-8000000000000000000000000000000000000000000000000000
χ588-888-88-8-8000000000000000000000000000000000000000000000000000
χ598-8-8-8-8888000000000000000000000000000000000000000000000000000

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