Finite Group Databasebeta

← Group #167594

Character table — Group #167594

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444442244444422444444488888888888888882444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-11-1-1-1-1
χ3111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-1-1
χ4111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-11-1-1-1-1-11111
χ5111111111111111111111111-1-1111-1-1111111111111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-11-111-11111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-11-1-111111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-11111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1-11111-1-1-1-11111-1-1-1-1111-111-1-11-1-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1111-1-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1111-11-1-1-11-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11-11-1-1-11-111111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11-1-1111-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111111-1-1-1-1111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-111111-111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1-111111-1-1-1-1-111
χ172222222222222222-2-2-2-222-2-222-200220000000000000000000-20000-2000000000
χ182222222222222222-2-2-2-222-2-2-2-2-200-2-20000000000000000000200002000000000
χ19222222222222-2-2-2-2222-2-2-22-200-20000000000000000000000200-20000-20020000
χ20222222222222-2-2-2-2222-2-2-22-200-20000000000000000000000-20020000200-20000
χ21222222222222-2-2-2-2-2-2-22-2-2-220022200-2-2000000000000000000-20000200000000
χ22222222222222-2-2-2-2-2-2-22-2-2-22002-2-2002200000000000000000020000-200000000
χ2322222222-2-2-2-2222222-22-2-2-2200-2220022000000000000000000-20000-200000000
χ2422222222-2-2-2-2222222-22-2-2-2200-2-2-200-2-200000000000000000020000200000000
χ2522222222-2-2-2-22222-2-22-2-2-22-2002000000000000000000000020020000-200-20000
χ2622222222-2-2-2-22222-2-22-2-2-22-20020000000000000000000000-200-2000020020000
χ2722222222-2-2-2-2-2-2-2-222-2-222-2-222200-2-20000000000000000000-200002000000000
χ2822222222-2-2-2-2-2-2-2-222-2-222-2-2-2-220022000000000000000000020000-2000000000
χ292-222-22-2-22i2i−2i−2i2i2i−2i−2i00002-2002-20002i−2i000000000022−2−2i2i2−i2−i20000000000002−2i2−i2
χ302-222-22-2-22i2i−2i−2i2i2i−2i−2i00002-2002-20002i−2i0000000000−2−222−i2−i2i2i2000000000000−22−i2i2
χ312-222-22-2-22i2i−2i−2i2i2i−2i−2i00002-200-22000−2i2i000000000022−2−2i2i2−i2−i2000000000000−22−i2i2
χ322-222-22-2-22i2i−2i−2i2i2i−2i−2i00002-200-22000−2i2i0000000000−2−222−i2−i2i2i20000000000002−2i2−i2
χ332-222-22-2-2−2i−2i2i2i−2i−2i2i2i00002-2002-2000−2i2i000000000022−2−2−i2−i2i2i20000000000002−2−i2i2
χ342-222-22-2-2−2i−2i2i2i−2i−2i2i2i00002-2002-2000−2i2i0000000000−2−222i2i2−i2−i2000000000000−22i2−i2
χ352-222-22-2-2−2i−2i2i2i−2i−2i2i2i00002-200-220002i−2i000000000022−2−2−i2−i2i2i2000000000000−22i2−i2
χ362-222-22-2-2−2i−2i2i2i−2i−2i2i2i00002-200-220002i−2i0000000000−2−222i2i2−i2−i20000000000002−2−i2i2
χ372-2-2-222-2200002-22-22-202000-20002-2002-2i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ382-2-2-222-2200002-22-22-202000-20002-2002-2−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ392-2-2-222-2200002-22-22-202000-2000-2200-22i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ402-2-2-222-2200002-22-22-202000-2000-2200-22−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ412-2-2-222-220000-22-22-2202000-20002-200-22i2i2−i2−i2−i2−i2i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ422-2-2-222-220000-22-22-2202000-20002-200-22−i2−i2i2i2i2i2−i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ432-2-2-222-220000-22-22-2202000-2000-22002-2i2i2−i2−i2−i2−i2i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ442-2-2-222-220000-22-22-2202000-2000-22002-2−i2−i2i2i2i2i2−i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ45444-44-4-4-400000000004000-4000000000022−2222−220000000000000000000000000000
χ46444-44-4-4-400000000004000-40000000000−2222−22220000000000000000000000000000
χ47444-44-4-4-40000000000-40004000000000000002i2−2i22i2−2i2000000000000000000000000
χ48444-44-4-4-40000000000-4000400000000000000−2i22i2−2i22i2000000000000000000000000
χ4944-44-4-4-444-44-4000000000000000000000000000000000000000002i−2i0002i−2i00000
χ5044-44-4-4-444-44-400000000000000000000000000000000000000000−2i2i000−2i2i00000
χ5144-44-4-4-44-44-44000000000000000000000000000000000000000002i−2i000−2i2i00000
χ5244-44-4-4-44-44-4400000000000000000000000000000000000000000−2i2i0002i−2i00000
χ5344-4-4-444-400004i−4i−4i4i00000000000000000000000002i−2i−2i2i-222-20000000000000000
χ5444-4-4-444-400004i−4i−4i4i0000000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ5544-4-4-444-40000−4i4i4i−4i00000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ5644-4-4-444-40000−4i4i4i−4i0000000000000000000000000−2i2i2i−2i-222-20000000000000000
χ574-444-44-4-44i4i−4i−4i−4i−4i4i4i0000-440000000000000000000000000000000000000000000
χ584-444-44-4-4−4i−4i4i4i4i4i−4i−4i0000-440000000000000000000000000000000000000000000
χ594-4-444-44-44i−4i−4i4i0000000000000000000002i−2i−2i2i2-2-22000000000000000000000000
χ604-4-444-44-44i−4i−4i4i000000000000000000000−2i2i2i−2i-222-2000000000000000000000000
χ614-4-444-44-4−4i4i4i−4i0000000000000000000002i−2i−2i2i-222-2000000000000000000000000
χ624-4-444-44-4−4i4i4i−4i000000000000000000000−2i2i2i−2i2-2-22000000000000000000000000
χ634-4-4-444-4400004-44-4-440-4000400000000000000000000000000000000000000000
χ644-4-4-444-440000-44-444-40-4000400000000000000000000000000000000000000000
χ658-88-8-8-888000000000000000000000000000000000000000000000000000000000

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