Finite Group Databasebeta

← Group #167472

Character table — Group #167472

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444488888888888888882244444444448888
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
χ3111111111111111111111111111-1-111-1-11111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1
χ4111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111
χ51111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-11-111-111-1-1-1-1
χ61111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1111-111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-11111-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-11-1111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-111-1-11111-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-11-1-1-1111-1-111
χ1111111111-1-1-1-1-1-1-1-111-1-11111-111-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-11-1-11-1-1111-1-111
χ1211111111-1-1-1-1-1-1-1-111-1-11111-111-1-1-1-111-1-1-1-11111-1-1-1-111111-1-11-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-111-1-11111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1111111-1-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-111-1-11111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111-11-1-1-1-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111-11-1-111-1-1-1-1-111
χ1722222222222222222-2-2-2-2-22-2-2002200220000000000000000-20000-20000000000
χ1822222222222222222-2-2-2-2-22-2-200-2-200-2-200000000000000002000020000000000
χ19222222222222-2-2-2-2-2222-2-2-22-200000000000000000000000002-2-2002000000000
χ20222222222222-2-2-2-2-2222-2-2-22-20000000000000000000000000-22200-2000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-222200-2-2000000000000000000000020000-2000000
χ22222222222222-2-2-2-2-2-2-2-222-2-22-2-200220000000000000000000000-200002000000
χ2322222222-2-2-2-22222-22-2-2-2-2-22200000000000000000000000002-2200-2000000000
χ2422222222-2-2-2-22222-22-2-2-2-2-2220000000000000000000000000-22-2002000000000
χ2522222222-2-2-2-22222-2-22222-2-2-22200220000000000000000000000-20000-2000000
χ2622222222-2-2-2-22222-2-22222-2-2-2-2-200-2-20000000000000000000000200002000000
χ2722222222-2-2-2-2-2-2-2-22-222-2-22-22002200-2-2000000000000000020000-20000000000
χ2822222222-2-2-2-2-2-2-2-22-222-2-22-2200-2-200220000000000000000-2000020000000000
χ29222-22-2-2-222-2-222-2-2-200000200002i−2i002i−2i00000000i2i2−i2−i2i2i2−i2−i20000000000002−22−2
χ30222-22-2-2-222-2-222-2-2-200000200002i−2i002i−2i00000000−i2−i2i2i2−i2−i2i2i2000000000000−22−22
χ31222-22-2-2-222-2-222-2-2-20000020000−2i2i00−2i2i00000000i2i2−i2−i2i2i2−i2−i2000000000000−22−22
χ32222-22-2-2-222-2-222-2-2-20000020000−2i2i00−2i2i00000000−i2−i2i2i2−i2−i2i2i20000000000002−22−2
χ33222-22-2-2-2-2-222-2-222-200000200002i−2i00−2i2i00000000i2i2−i2−i2−i2−i2i2i20000000000002−2−22
χ34222-22-2-2-2-2-222-2-222-200000200002i−2i00−2i2i00000000−i2−i2i2i2i2i2−i2−i2000000000000−222−2
χ35222-22-2-2-2-2-222-2-222-20000020000−2i2i002i−2i00000000i2i2−i2−i2−i2−i2i2i2000000000000−222−2
χ36222-22-2-2-2-2-222-2-222-20000020000−2i2i002i−2i00000000−i2−i2i2i2i2i2−i2−i20000000000002−2−22
χ3722-22-2-2-2200002i−2i2i−2i002i−2i2-20002i−2i002-20022−2−2i2i2−i2−i2i2−i2i2−i22−22−20000000000000000
χ3822-22-2-2-2200002i−2i2i−2i002i−2i2-20002i−2i002-200−2−222−i2−i2i2i2−i2i2−i2i2−22−220000000000000000
χ3922-22-2-2-2200002i−2i2i−2i002i−2i2-2000−2i2i00-220022−2−2i2i2−i2−i2−i2i2−i2i2−22−220000000000000000
χ4022-22-2-2-2200002i−2i2i−2i002i−2i2-2000−2i2i00-2200−2−222−i2−i2i2i2i2−i2i2−i22−22−20000000000000000
χ4122-22-2-2-220000−2i2i−2i2i00−2i2i2-20002i−2i00-220022−2−2−i2−i2i2i2i2−i2i2−i2−22−220000000000000000
χ4222-22-2-2-220000−2i2i−2i2i00−2i2i2-20002i−2i00-2200−2−222i2i2−i2−i2−i2i2−i2i22−22−20000000000000000
χ4322-22-2-2-220000−2i2i−2i2i00−2i2i2-2000−2i2i002-20022−2−2−i2−i2i2i2−i2i2−i2i22−22−20000000000000000
χ4422-22-2-2-220000−2i2i−2i2i00−2i2i2-2000−2i2i002-200−2−222i2i2−i2−i2i2−i2i2−i2−22−220000000000000000
χ45444-44-4-4-444-4-4-4-444400000-4000000000000000000000000000000000000000000
χ46444-44-4-4-4-4-44444-4-4400000-4000000000000000000000000000000000000000000
χ4744-44-4-4-4400004i−4i4i−4i00−4i4i-440000000000000000000000000000000000000000000
χ4844-44-4-4-440000−4i4i−4i4i004i−4i-440000000000000000000000000000000000000000000
χ4944-4-4-444-400004i−4i−4i4i00000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ5044-4-4-444-400004i−4i−4i4i0000000000000000000000000-222-22i−2i−2i2i0000000000000000
χ5144-4-4-444-40000−4i4i4i−4i00000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ5244-4-4-444-40000−4i4i4i−4i0000000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ534-44-4-44-44000000000400000-400000000000002i2−2i22i2−2i2000000000000000000000000
χ544-44-4-44-44000000000400000-40000000000000−2i22i2−2i22i2000000000000000000000000
χ554-44-4-44-44000000000-400000400000000022−2222−220000000000000000000000000000
χ564-44-4-44-44000000000-4000004000000000−2222−22220000000000000000000000000000
χ574-4-4444-4-44-44-4000000000000000000000000000000000000000000002i−2i02i−2i0000
χ584-4-4444-4-44-44-400000000000000000000000000000000000000000000−2i2i0−2i2i0000
χ594-4-4444-4-4-44-44000000000000000000000000000000000000000000002i−2i0−2i2i0000
χ604-4-4444-4-4-44-4400000000000000000000000000000000000000000000−2i2i02i−2i0000
χ614-4-4-44-4444-4-440000000000000000000002-2-222-2-22000000000000000000000000
χ624-4-4-44-4444-4-44000000000000000000000-222-2-222-2000000000000000000000000
χ634-4-4-44-444-444-40000000000000000000002-2-22-222-2000000000000000000000000
χ644-4-4-44-444-444-4000000000000000000000-222-22-2-22000000000000000000000000
χ658-888-8-88-8000000000000000000000000000000000000000000000000000000000

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