Finite Group Databasebeta

← Group #176147

Character table — Group #176147

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222444444444444444422444444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1111-1111-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-11-1-1-1-1-11-1-11111-1-1-1-11111
χ51111111111111111111-1-11-1-11-111-1-111-111-11-1-1-1-1-1-1-1-1-11111
χ61111111111111111111-1-11-1-11-111-1-1-1-1-1-1-1-11-111111111-1-1-1-1
χ71111111111111111111-1-11-1-1-11-1-11-111111-1-111111-1-1-1-1-1-1-1-1
χ81111111111111111111-1-11-1-1-11-1-11-1-1-11-1-1-1-11-1-1-1-111111111
χ9111111111-1-11-1-11111-111-1-1-1111-11-111-1-1-11-1-111-1-111-1-111-1-1
χ10111111111-1-11-1-11111-111-1-1-1111-11-1-1-1-1111-1-1-1-111-1-111-1-111
χ11111111111-1-11-1-11111-111-1-1-1-1-1-11-1-1111-1-1111-1-11111-1-1-1-111
χ12111111111-1-11-1-11111-111-1-1-1-1-1-11-1-1-1-111111111-1-1-1-11111-1-1
χ13111111111-1-11-1-11111-1-1-1-1111-11-1-11111-1-1-1-11-1-111-1-11111-1-1
χ14111111111-1-11-1-11111-1-1-1-1111-11-1-11-1-1111-1-1111-1-111-1-1-1-111
χ15111111111-1-11-1-11111-1-1-1-111-11-111111-1-1-1-11-111-1-1-1-111-1-111
χ16111111111-1-11-1-11111-1-1-1-111-11-1111-1-1-111-11-1-1-11111-1-111-1-1
χ1722222222222-2-2-2-2-22-2-20020020-2200000000-20000000000000
χ1822222222222-2-2-2-2-22-2-200200-202-20000000020000000000000
χ19222222222-2-2-222-2-22-2200-20020-2-20000000020000000000000
χ20222222222-2-2-222-2-22-2200-200-202200000000-20000000000000
χ2122222222-2222-2-2-2-2-22222-2-2-200000200000-200000000000000
χ2222222222-2222-2-2-2-2-222-2-2-22200000-200000200000000000000
χ2322222222-222-22222-2-2-200-2000200-2000-200002000000000000
χ2422222222-222-22222-2-2-200-2000-200200020000-2000000000000
χ2522222222-2-2-2222-2-2-22-22222200000-200000-200000000000000
χ2622222222-2-2-2222-2-2-22-2-2-22-2-200000200000200000000000000
χ2722222222-2-2-2-2-2-222-2-22002000200-200020000-2000000000000
χ2822222222-2-2-2-2-2-222-2-22002000-2002000-200002000000000000
χ29444-44-4-4-4000400000-404-400000000000000000000000000000
χ30444-44-4-4-4000400000-40-4400000000000000000000000000000
χ31444-44-4-4-4000-400000400004i−4i00000000000000000000000000
χ32444-44-4-4-4000-40000040000−4i4i00000000000000000000000000
χ3344-44-44-4-440000000-400000000000000000000022−220000000000
χ3444-44-44-4-440000000-4000000000000000000000−22220000000000
χ3544-44-44-4-4-400000004000000000000000000000002i2−2i200000000
χ3644-44-44-4-4-40000000400000000000000000000000−2i22i200000000
χ374-444-4-4-4404-4000000000000000000000000000000000002i−2i2i−2i
χ384-444-4-4-4404-400000000000000000000000000000000000−2i2i−2i2i
χ394-444-4-4-440-44000000000000000000000000000000000002i−2i−2i2i
χ404-444-4-4-440-4400000000000000000000000000000000000−2i2i2i−2i
χ414-44-4-444-40000004-400000000000000000000000000002i2−2i20000
χ424-44-4-444-40000004-40000000000000000000000000000−2i22i20000
χ434-44-4-444-4000000-44000000000000000000000000002i2−2i2000000
χ444-44-4-444-4000000-4400000000000000000000000000−2i22i2000000
χ454-4-444-44-400004i−4i00000000000000002i−2i02-2000000000000000
χ464-4-444-44-400004i−4i0000000000000000−2i2i0-22000000000000000
χ474-4-444-44-40000−4i4i00000000000000002i−2i0-22000000000000000
χ484-4-444-44-40000−4i4i0000000000000000−2i2i02-2000000000000000
χ4988-8-8-8-888000000000000000000000000000000000000000000
χ508-8-8-888-88000000000000000000000000000000000000000000

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