Finite Group Databasebeta

← Group #167712

Character table — Group #167712

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444444444444488888888888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1
χ3111111111111111111111111111-1-111-1-111111111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-111-1111111
χ51111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ61111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-11-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-11-1-1-1-1-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-11-111-111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-1-1111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-11-111-1-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-111-1-1-1-11111-1-1-1-111111-1-11-11111-1-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1111-1111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1111-1-1-111111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-11-11-1-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-11-1111-1-1-1-1-111
χ172222222222222222-2-2-2-2-222-2-2002200220000000000000000000000-200-2000000
χ182222222222222222-2-2-2-2-222-2-200-2-200-2-200000000000000000000002002000000
χ19222222222222-2-2-2-2222-2-2-2-22-2220022000000000000000000-2000-200000000000
χ20222222222222-2-2-2-2222-2-2-2-22-2-2-200-2-20000000000000000002000200000000000
χ21222222222222-2-2-2-2-2-2-222-2-2-2200000000000000000000000002-2-2020000000000
χ22222222222222-2-2-2-2-2-2-222-2-2-220000000000000000000000000-2220-20000000000
χ2322222222-2-2-2-2222222-222-2-2-2-200000000000000000000000002-220-20000000000
χ2422222222-2-2-2-2222222-222-2-2-2-20000000000000000000000000-22-2020000000000
χ2522222222-2-2-2-22222-2-22-2-2-2-2222200-2-2000000000000000000-2000200000000000
χ2622222222-2-2-2-22222-2-22-2-2-2-222-2-200220000000000000000002000-200000000000
χ2722222222-2-2-2-2-2-2-2-222-2-2-222-22002200-2-20000000000000000000000200-2000000
χ2822222222-2-2-2-2-2-2-2-222-2-2-222-2200-2-200220000000000000000000000-2002000000
χ292-222-22-2-222-2-200002-2-20000202i−2i002i−2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i20000000000000000
χ302-222-22-2-222-2-200002-2-20000202i−2i002i−2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i20000000000000000
χ312-222-22-2-222-2-200002-2-2000020−2i2i00−2i2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i20000000000000000
χ322-222-22-2-222-2-200002-2-2000020−2i2i00−2i2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i20000000000000000
χ332-222-22-2-2-2-2220000-22-20000202i−2i00−2i2i0022−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ342-222-22-2-2-2-2220000-22-20000202i−2i00−2i2i00−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ352-222-22-2-2-2-2220000-22-2000020−2i2i002i−2i0022−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ362-222-22-2-2-2-2220000-22-2000020−2i2i002i−2i00−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ372-22-22-22-22i−2i2i−2i2i2i−2i−2i000002-200002-2002i−2i000000002−22−2i2−i2i2−i20000000000002−2i2−i2
χ382-22-22-22-22i−2i2i−2i2i2i−2i−2i000002-200002-2002i−2i00000000−22−22−i2i2−i2i2000000000000−22−i2i2
χ392-22-22-22-22i−2i2i−2i2i2i−2i−2i000002-20000-2200−2i2i000000002−22−2i2−i2i2−i2000000000000−22−i2i2
χ402-22-22-22-22i−2i2i−2i2i2i−2i−2i000002-20000-2200−2i2i00000000−22−22−i2i2−i2i20000000000002−2i2−i2
χ412-22-22-22-2−2i2i−2i2i−2i−2i2i2i000002-200002-200−2i2i000000002−22−2−i2i2−i2i20000000000002−2−i2i2
χ422-22-22-22-2−2i2i−2i2i−2i−2i2i2i000002-200002-200−2i2i00000000−22−22i2−i2i2−i2000000000000−22i2−i2
χ432-22-22-22-2−2i2i−2i2i−2i−2i2i2i000002-20000-22002i−2i000000002−22−2−i2i2−i2i2000000000000−22i2−i2
χ442-22-22-22-2−2i2i−2i2i−2i−2i2i2i000002-20000-22002i−2i00000000−22−22i2−i2i2−i20000000000002−2−i2i2
χ45444-4-4-4-444i−4i−4i4i000000000000000000000000000002i−2i−2i2i-222-20000000000000000
χ46444-4-4-4-444i−4i−4i4i00000000000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ47444-4-4-4-44−4i4i4i−4i000000000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ48444-4-4-4-44−4i4i4i−4i00000000000000000000000000000−2i2i2i−2i-222-20000000000000000
χ4944-444-4-4-4000000000004-4000000000000000022−2222−22000000000000000000000000
χ5044-444-4-4-4000000000004-40000000000000000−2222−2222000000000000000000000000
χ5144-444-4-4-400000000000-4400000000000022−2222−220000000000000000000000000000
χ5244-444-4-4-400000000000-44000000000000−2222−22220000000000000000000000000000
χ5344-4-4-444-400004i−4i4i−4i00000000000000000000000000000000000000002-202i−2i0000
χ5444-4-4-444-400004i−4i4i−4i0000000000000000000000000000000000000000-220−2i2i0000
χ5544-4-4-444-40000−4i4i−4i4i00000000000000000000000000000000000000002-20−2i2i0000
χ5644-4-4-444-40000−4i4i−4i4i0000000000000000000000000000000000000000-2202i−2i0000
χ574-444-44-4-444-4-40000-4440000-400000000000000000000000000000000000000000
χ584-444-44-4-4-4-44400004-440000-400000000000000000000000000000000000000000
χ594-44-44-44-44i−4i4i−4i−4i−4i4i4i00000-44000000000000000000000000000000000000000000
χ604-44-44-44-4−4i4i−4i4i4i4i−4i−4i00000-44000000000000000000000000000000000000000000
χ614-4-44-4-44400004-4-44000000000000000002-2-222-2-22000000000000000000000000
χ624-4-44-4-44400004-4-4400000000000000000-222-2-222-2000000000000000000000000
χ634-4-44-4-4440000-444-4000000000000000002-2-22-222-2000000000000000000000000
χ644-4-44-4-4440000-444-400000000000000000-222-22-2-22000000000000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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