Finite Group Databasebeta

← Group #175012

Character table — Group #175012

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444444444444224444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-11-11-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ411111111111111111111111-1-111-1-11-11-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111-1-111-1-111-11-1-1-1-11-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111-1-111-1-111-11-1-1-1-11-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-1-1111-111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-1-11111-1-1-1-11111
χ9111111111-1-1-1-1-1-111111-11111-1-1-1-1-1111-11-1-111-1-111-1-111-1-111-1-1
χ10111111111-1-1-1-1-1-111111-11111-1-1-1-1-1111-11-1-1-1-111-1-111-1-111-1-111
χ11111111111-1-1-1-1-1-111111-111-1-1-1-111-1-11-11-11111-1-1-1-111-1-11111-1-1
χ12111111111-1-1-1-1-1-111111-111-1-1-1-111-1-11-11-111-1-11111-1-111-1-1-1-111
χ13111111111-1-1-1-1-1-111111-1-1-11111-1-111-1-11-1-1111-1-111-1-1-1-111-1-111
χ14111111111-1-1-1-1-1-111111-1-1-11111-1-111-1-11-1-11-1-111-1-11111-1-111-1-1
χ15111111111-1-1-1-1-1-111111-1-1-1-1-111111-1-11-111-111-1-1-1-11111-1-1-1-111
χ16111111111-1-1-1-1-1-111111-1-1-1-1-111111-1-11-111-1-1-11111-1-1-1-11111-1-1
χ172222222222222-2-2-2-2-2-22-22200-2-20020-2000000000000000000000
χ182222222222222-2-2-2-2-2-22-2-2-2002200-202000000000000000000000
χ19222222222-2-2-2-222-2-2-2-22222002200-20-2000000000000000000000
χ20222222222-2-2-2-222-2-2-2-222-2-200-2-200202000000000000000000000
χ2122222222-222-2-22222-2-2-2-2002200220-20000-200000000000000000
χ2222222222-222-2-22222-2-2-2-200-2-200-2-2020000200000000000000000
χ2322222222-222-2-2-2-2-2-222-220000000000022-20-20000000000000000
χ2422222222-222-2-2-2-2-2-222-2200000000000-2-22020000000000000000
χ2522222222-2-2-22222-2-222-2-2000000000002-2-2020000000000000000
χ2622222222-2-2-22222-2-222-2-200000000000-2220-20000000000000000
χ2722222222-2-2-222-2-222-2-2-22002200-2-20-20000200000000000000000
χ2822222222-2-2-222-2-222-2-2-2200-2-20022020000-200000000000000000
χ29444-4-44-4-440000000000-404-4000000000000000000000000000000
χ30444-4-44-4-440000000000-40-44000000000000000000000000000000
χ31444-4-44-4-4-400000000004000004i−4i00000000000000000000000000
χ32444-4-44-4-4-40000000000400000−4i4i00000000000000000000000000
χ3344-44-4-44-40004i−4i0000000000000000000000000000000000002i−2i2-2
χ3444-44-4-44-40004i−4i000000000000000000000000000000000000−2i2i-22
χ3544-44-4-44-4000−4i4i0000000000000000000000000000000000002i−2i-22
χ3644-44-4-44-4000−4i4i000000000000000000000000000000000000−2i2i2-2
χ3744-4-44-4-4404i−4i000000000000000000000000002i−2i2-2000000000000
χ3844-4-44-4-4404i−4i00000000000000000000000000−2i2i-22000000000000
χ3944-4-44-4-440−4i4i000000000000000000000000002i−2i-22000000000000
χ4044-4-44-4-440−4i4i00000000000000000000000000−2i2i2-2000000000000
χ414-444-4-4-44000004i−4i0000000000000000000000000000002-22i−2i0000
χ424-444-4-4-44000004i−4i000000000000000000000000000000-22−2i2i0000
χ434-444-4-4-4400000−4i4i0000000000000000000000000000002-2−2i2i0000
χ444-444-4-4-4400000−4i4i000000000000000000000000000000-222i−2i0000
χ454-44-44-44-400000004-400000000004i−4i000000000000000000000000
χ464-44-44-44-400000004-40000000000−4i4i000000000000000000000000
χ474-44-44-44-40000000-440000004i−4i0000000000000000000000000000
χ484-44-44-44-40000000-44000000−4i4i0000000000000000000000000000
χ494-4-4-4-44440000000004-400000000000000000000000022−2200000000
χ504-4-4-4-44440000000004-4000000000000000000000000−222200000000
χ514-4-4-4-4444000000000-44000000000000000000000022−220000000000
χ524-4-4-4-4444000000000-440000000000000000000000−22220000000000
χ538-8-8888-8-8000000000000000000000000000000000000000000000

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