Finite Group Databasebeta

← Group #177709

Character table — Group #177709

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size11111111444444448888888161616161616161616161616161616161616161616163232
order12222222444444444444444224444444488888888888844
χ111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-1-1-111-1-1-111-1-11-11111-1-1-1-11111-1-1
χ6111111111111111111-1-1-1-111-1-1-111-1-11-1-1-1-1-11111-1-1-1-111
χ7111111111111111111-1-1-1-11-11-1-1-1-111-111111-1-1-1-1-1-1-1-111
χ8111111111111111111-1-1-1-11-11-1-1-1-111-11-1-1-1-111111111-1-1
χ9111111111-1-111111-1-111-1-1-1111-11-11-1-1-111-1-111-1-111-1-11-1
χ10111111111-1-111111-1-111-1-1-1111-11-11-1-1-1-1-111-1-111-1-111-11
χ11111111111-1-111111-1-111-1-1-1-1-11-1-11-111111-1-111-1-1-1-111-11
χ12111111111-1-111111-1-111-1-1-1-1-11-1-11-1111-1-111-1-11111-1-11-1
χ13111111111-1-111111-1-1-1-111-11-1-111-1-11-1111-1-1-1-11111-1-1-11
χ14111111111-1-111111-1-1-1-111-11-1-111-1-11-11-1-11111-1-1-1-1111-1
χ15111111111-1-111111-1-1-1-111-1-11-11-111-11-111-1-1-1-111-1-1111-1
χ16111111111-1-111111-1-1-1-111-1-11-11-111-11-1-1-11111-1-111-1-1-11
χ1722222222222-2-2-2-22-2-22222200-2-200000000000000000000
χ1822222222222-2-2-2-22-2-2-2-2-2-22002200000000000000000000
χ19222222222-2-2-2-2-2-222222-2-2-200-2200000000000000000000
χ20222222222-2-2-2-2-2-2222-2-222-2002-200000000000000000000
χ2122222222-22222-2-2-22-20000-2020000-2-20200000000000000
χ2222222222-22222-2-2-22-20000-20-20000220-200000000000000
χ2322222222-222-2-222-2-220000-22000-2-2002000000000000000
χ2422222222-222-2-222-2-220000-2-20002200-2000000000000000
χ2522222222-2-2-222-2-2-2-2200002020000-220-200000000000000
χ2622222222-2-2-222-2-2-2-22000020-200002-20200000000000000
χ2722222222-2-2-2-2-222-22-2000022000-2200-2000000000000000
χ2822222222-2-2-2-2-222-22-200002-20002-2002000000000000000
χ29444-4-4-4-4404-40000000000000000000000000000002i−2i2i−2i00
χ30444-4-4-4-4404-4000000000000000000000000000000−2i2i−2i2i00
χ31444-4-4-4-440-440000000000000000000000000000002i−2i−2i2i00
χ32444-4-4-4-440-44000000000000000000000000000000−2i2i2i−2i00
χ3344-444-4-4-44000000-4004-4000000000000000000000000000
χ3444-444-4-4-44000000-400-44000000000000000000000000000
χ3544-444-4-4-4-4000000400004i−4i0000000000000000000000000
χ3644-444-4-4-4-400000040000−4i4i0000000000000000000000000
χ374-4-44-44-44000004-40000000000000000000022−220000000000
χ384-4-44-44-44000004-400000000000000000000−22220000000000
χ394-4-44-44-4400000-4400000000000000000022−22000000000000
χ404-4-44-44-4400000-44000000000000000000−2222000000000000
χ414-4-4-44-4440004-40000000000000000000000000022−22000000
χ424-4-4-44-4440004-400000000000000000000000000−2222000000
χ434-4-4-44-444000-4400000000000000000000000022−2200000000
χ444-4-4-44-444000-44000000000000000000000000−222200000000
χ4588-8-8-888-8000000000000000000000000000000000000000
χ468-888-8-88-8000000000000000000000000000000000000000
χ478-88-888-8-8000000000000000000000000000000000000000

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