Finite Group Databasebeta

← Group #166993

Character table — Group #166993

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444422224444488888888888888882222444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111-1-1111-1-111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-11-1-1111111
χ5111111111111111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ6111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-11-111-1-11111
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-11-11111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11111-111-1-1-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-11-111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-111111-1-111
χ1211111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-11-1111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-11-1-111111-1-111-111-1-11111-1-1-1-1-1-1-1-111111-1111-1-1-111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-11-1-111111-1-111-111-1-1-1-1-1-111111111-1-1-1-11-1-1-11-1-1-1111111-1-1
χ1511111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-111-1-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-111-1-1-1-1-1-1-111
χ172222222222222222-2-2-22-2-2-220022-2002200000000000000000000-2-20000000000
χ182222222222222222-2-2-22-2-2-2200-2-2-200-2-200000000000000000000220000000000
χ19222222222222-2-2-2-2222-2-2-22-20000-200000000000000000000020000-20-22000000
χ20222222222222-2-2-2-2222-2-2-22-20000-2000000000000000000000-20000202-2000000
χ21222222222222-2-2-2-2-2-2-2-222-2-222002-2-20000000000000000002000000-200000000
χ22222222222222-2-2-2-2-2-2-2-222-2-2-2-200222000000000000000000-2000000200000000
χ2322222222-2-2-2-222222-2-2-2-2-22-20000200000000000000000000020000-202-2000000
χ2422222222-2-2-2-222222-2-2-2-2-22-200002000000000000000000000-2000020-22000000
χ2522222222-2-2-2-22222-222-222-2-22200-222000000000000000000-2000000-200000000
χ2622222222-2-2-2-22222-222-222-2-2-2-200-2-2-20000000000000000002000000200000000
χ2722222222-2-2-2-2-2-2-2-2-2222-2-2-220022200-2-200000000000000000000-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2222-2-2-2200-2-220022000000000000000000002-20000000000
χ292222-2-2-2-200002i2i−2i−2i02i−2i02-2002-20002i−2i0022−2−2i2i2−i2−i222−2−2i2i2−i2−i20000000000000000
χ302222-2-2-2-200002i2i−2i−2i02i−2i02-2002-20002i−2i00−2−222−i2−i2i2i2−2−222−i2−i2i2i20000000000000000
χ312222-2-2-2-200002i2i−2i−2i02i−2i02-200-22000−2i2i0022−2−2i2i2−i2−i2−2−222−i2−i2i2i20000000000000000
χ322222-2-2-2-200002i2i−2i−2i02i−2i02-200-22000−2i2i00−2−222−i2−i2i2i222−2−2i2i2−i2−i20000000000000000
χ332222-2-2-2-20000−2i−2i2i2i0−2i2i02-2002-2000−2i2i0022−2−2−i2−i2i2i222−2−2−i2−i2i2i20000000000000000
χ342222-2-2-2-20000−2i−2i2i2i0−2i2i02-2002-2000−2i2i00−2−222i2i2−i2−i2−2−222i2i2−i2−i20000000000000000
χ352222-2-2-2-20000−2i−2i2i2i0−2i2i02-200-220002i−2i0022−2−2−i2−i2i2i2−2−222i2i2−i2−i20000000000000000
χ362222-2-2-2-20000−2i−2i2i2i0−2i2i02-200-220002i−2i00−2−222i2i2−i2−i222−2−2−i2−i2i2i20000000000000000
χ3722-2-2-2-22222-2-22-22-2000-20002002-20002-2000000002−22−22−22−20000000000002−22−2
χ3822-2-2-2-22222-2-22-22-2000-20002002-20002-200000000−22−22−22−22000000000000−22−22
χ3922-2-2-2-22222-2-22-22-2000-2000200-22000-22000000002−22−22−22−2000000000000−22−22
χ4022-2-2-2-22222-2-22-22-2000-2000200-22000-2200000000−22−22−22−220000000000002−22−2
χ4122-2-2-2-222-2-222-22-22000-20002002-2000-22000000002−22−2−22−220000000000002−2−22
χ4222-2-2-2-222-2-222-22-22000-20002002-2000-2200000000−22−222−22−2000000000000−222−2
χ4322-2-2-2-222-2-222-22-22000-2000200-220002-2000000002−22−2−22−22000000000000−222−2
χ4422-2-2-2-222-2-222-22-22000-2000200-220002-200000000−22−222−22−20000000000002−2−22
χ454444-4-4-4-400004i4i−4i−4i0−4i4i0-440000000000000000000000000000000000000000000
χ464444-4-4-4-40000−4i−4i4i4i04i−4i0-440000000000000000000000000000000000000000000
χ4744-4-444-4-400004i−4i−4i4i00000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ4844-4-444-4-400004i−4i−4i4i0000000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ4944-4-444-4-40000−4i4i4i−4i00000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ5044-4-444-4-40000−4i4i4i−4i0000000000000000000000000-222-22i−2i−2i2i0000000000000000
χ5144-4-4-4-44444-4-4-44-440004000-400000000000000000000000000000000000000000
χ5244-4-4-4-444-4-4444-44-40004000-400000000000000000000000000000000000000000
χ534-44-44-44-400000000400000-4000000000000002i2−2i22i2−2i2000000000000000000000000
χ544-44-44-44-400000000400000-400000000000000−2i22i2−2i22i2000000000000000000000000
χ554-44-44-44-400000000-4000004000000000022−2222−220000000000000000000000000000
χ564-44-44-44-400000000-40000040000000000−2222−22220000000000000000000000000000
χ574-44-4-44-444-44-40000000000000000000002-2-222-2-22000000000000000000000000
χ584-44-4-44-444-44-4000000000000000000000-222-2-222-2000000000000000000000000
χ594-44-4-44-44-44-440000000000000000000002-2-22-222-2000000000000000000000000
χ604-44-4-44-44-44-44000000000000000000000-222-22-2-22000000000000000000000000
χ614-4-444-4-444-4-440000000000000000000000000000000000000002-20000002-20000
χ624-4-444-4-444-4-44000000000000000000000000000000000000000-22000000-220000
χ634-4-444-4-44-444-40000000000000000000000000000000000000002-2000000-220000
χ644-4-444-4-44-444-4000000000000000000000000000000000000000-220000002-20000
χ658-8-88-888-8000000000000000000000000000000000000000000000000000000000

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