Finite Group Databasebeta

← Group #172015

Character table — Group #172015

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444422444444444422444444444488888888222244444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-1-1-1111111111-1-1-1-1-11-1-1-1-1-1-1-11111
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-1111111-1-1-1-1
χ5111111111111111111111111-1-111-1-1-1-111-1-111111111-11-1-1-1-1-11-1-11111-1-1-1-1
χ6111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1111-1-1-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-11111111111-1-11111-1-111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ911111111-1-1-1-1-1-1-1-11-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1111-111-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-11111-11-1-1-111-111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11111-1-11111-1-1
χ1211111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-11111-1-1-1-11111-1-1111-111-1-111-1-1-1-111
χ1311111111-1-1-1-1-1-1-1-11-1-111111-1-111-1-111-1-1111111-1-1-1-111-1-11-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-11-1-111111-1-111-1-111-1-111-1-1-1-1111111111-1-1-1-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1111111-1-11111-1-1-1-11-111-11-11-1-1-1-111-1-111
χ1611111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-11-111111-1-111-1-1
χ1722222222222222-2-22-2-2-2-2-2-22002200002200000000000-200000-20000000000
χ1822222222222222-2-22-2-2-2-2-2-2200-2-20000-2-20000000000020000020000000000
χ19222222222222-2-222-2-2-2-2-222-20000220000-2-20000000000002-2000000000000
χ20222222222222-2-222-2-2-2-2-222-20000-2-2000022000000000000-22000000000000
χ21222222222222-2-2-2-2-22222-2-2-222000022000000000000-200000-200000000000
χ22222222222222-2-2-2-2-22222-2-2-2-2-20000-2-2000000000000200000200000000000
χ2322222222-2-2-2-22222-2-2-222-2-2-2220000-2-2000000000000200000-200000000000
χ2422222222-2-2-2-22222-2-2-222-2-2-2-2-2000022000000000000-200000200000000000
χ2522222222-2-2-2-222-2-2-222-2-222-2000022000022000000000000-2-2000000000000
χ2622222222-2-2-2-222-2-2-222-2-222-20000-2-20000-2-200000000000022000000000000
χ2722222222-2-2-2-2-2-222222-2-2-2-2200220000-2-200000000000-20000020000000000
χ2822222222-2-2-2-2-2-222222-2-2-2-2200-2-200002200000000000200000-20000000000
χ2922-222-2-2-22i2i−2i−2i000002i−2i2-20002-200002i−2i000022−2−2i2i2−i2−i2000000000000002−2i2−i2
χ3022-222-2-2-22i2i−2i−2i000002i−2i2-20002-200002i−2i0000−2−222−i2−i2i2i200000000000000−22−i2i2
χ3122-222-2-2-22i2i−2i−2i000002i−2i2-2000-220000−2i2i000022−2−2i2i2−i2−i200000000000000−22−i2i2
χ3222-222-2-2-22i2i−2i−2i000002i−2i2-2000-220000−2i2i0000−2−222−i2−i2i2i2000000000000002−2i2−i2
χ3322-222-2-2-2−2i−2i2i2i00000−2i2i2-20002-20000−2i2i000022−2−2−i2−i2i2i2000000000000002−2−i2i2
χ3422-222-2-2-2−2i−2i2i2i00000−2i2i2-20002-20000−2i2i0000−2−222i2i2−i2−i200000000000000−22i2−i2
χ3522-222-2-2-2−2i−2i2i2i00000−2i2i2-2000-2200002i−2i000022−2−2−i2−i2i2i200000000000000−22i2−i2
χ3622-222-2-2-2−2i−2i2i2i00000−2i2i2-2000-2200002i−2i0000−2−222i2i2−i2−i2000000000000002−2−i2i2
χ3722-2-2-222-22-22-22-2002000000-2002i−2i00002i−2i00i2−i2i2−i2i2−i2i2−i200000000002−22−20000
χ3822-2-2-222-22-22-22-2002000000-2002i−2i00002i−2i00−i2i2−i2i2−i2i2−i2i20000000000−22−220000
χ3922-2-2-222-22-22-22-2002000000-200−2i2i0000−2i2i00i2−i2i2−i2i2−i2i2−i20000000000−22−220000
χ4022-2-2-222-22-22-22-2002000000-200−2i2i0000−2i2i00−i2i2−i2i2−i2i2−i2i200000000002−22−20000
χ4122-2-2-222-2-22-22-22002000000-2002i−2i0000−2i2i00i2−i2i2−i2−i2i2−i2i200000000002−2−220000
χ4222-2-2-222-2-22-22-22002000000-2002i−2i0000−2i2i00−i2i2−i2i2i2−i2i2−i20000000000−222−20000
χ4322-2-2-222-2-22-22-22002000000-200−2i2i00002i−2i00i2−i2i2−i2−i2i2−i2i20000000000−222−20000
χ4422-2-2-222-2-22-22-22002000000-200−2i2i00002i−2i00−i2i2−i2i2i2−i2i2−i200000000002−2−220000
χ45444-4-4-4-444i−4i−4i4i0000000000000000000000002i−2i−2i2i-222-2000000000000000000
χ46444-4-4-4-444i−4i−4i4i000000000000000000000000−2i2i2i−2i2-2-22000000000000000000
χ47444-4-4-4-44−4i4i4i−4i0000000000000000000000002i−2i−2i2i2-2-22000000000000000000
χ48444-4-4-4-44−4i4i4i−4i000000000000000000000000−2i2i2i−2i-222-2000000000000000000
χ4944-444-4-4-44i4i−4i−4i00000−4i4i-4400000000000000000000000000000000000000000
χ5044-444-4-4-4−4i−4i4i4i000004i−4i-4400000000000000000000000000000000000000000
χ5144-4-4-444-44-44-4-4400-4000000400000000000000000000000000000000000000
χ5244-4-4-444-4-44-444-400-4000000400000000000000000000000000000000000000
χ534-4-44-44-440000004-40000000000000000000000000000002-200002-200000000
χ544-4-44-44-440000004-4000000000000000000000000000000-220000-2200000000
χ554-4-44-44-44000000-440000000000000000000000000000002-20000-2200000000
χ564-4-44-44-44000000-44000000000000000000000000000000-2200002-200000000
χ574-4-4-44-44400000000000004-4000000000004-400000000000000000000000000
χ584-4-4-44-44400000000000004-400000000000-4400000000000000000000000000
χ594-4-4-44-4440000000000000-44000004-400000000000000000000000000000000
χ604-4-4-44-4440000000000000-4400000-4400000000000000000000000000000000
χ618-888-8-88-8000000000000000000000000000000000000000000000000000000
χ628-88-888-8-8000000000000000000000000000000000000000000000000000000

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