Finite Group Databasebeta

← Group #345670

Character table — Group #345670

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222222224488888888888888888888161616161616161616161616161616163232
order12222222444444444444444444888888888888444444448888888844
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-11111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-1-1-11-1
χ31111111111111111111111-1-111-1-1-1-11111-1-1-1-1-11-1-11111-1-111-1-1-1-11-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111
χ511111111111111111111-1-111111111-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-111-1-1-11
χ611111111111111111111-1-111-1-11111111111111-1-1-1-1-11-1-1-111-1-111-1-1
χ711111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1111111-111-1-1-1-111-1-1
χ811111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11-1111111-1-1-11
χ9111111111111111111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-11-1-1-1-1-1-111-11
χ10111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111-11111-11-1-11111-1-1-1-1
χ11111111111111111111-1-111-1-111111111111111-11-1-1-1-1-1111-1-111-1-1-1-1
χ12111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111111-1-111-11
χ13111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111
χ14111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-111-1-111-1-111111-1
χ15111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111111-1
χ16111111111111111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-111
χ172222222222-2-222-2-2-2-200220022000022-2-200000-200000-20000000000
χ182222222222-2-222-2-2-2-2002200-2-20000-2-22200000200000-20000000000
χ192222222222-2-222-2-2-2-200-2-200220000-2-22200000-20000020000000000
χ202222222222-2-222-2-2-2-200-2-200-2-2000022-2-20000020000020000000000
χ2122222222-2-222-2-222-2-22200220022-2-200000000-200000-200000000000
χ2222222222-2-222-2-222-2-22200-2-200-2-22200000000200000-200000000000
χ2322222222-2-222-2-222-2-2-2-2002200-2-22200000000-200000200000000000
χ2422222222-2-222-2-222-2-2-2-200-2-20022-2-200000000200000200000000000
χ2522-2-222-2-22222-2-2-2-2-22000000000000000022-2-2002-22-2000000000000
χ2622-2-222-2-22222-2-2-2-2-22000000000000000022-2-200-22-22000000000000
χ2722-2-222-2-22222-2-2-2-2-220000000000000000-2-222002-2-22000000000000
χ2822-2-222-2-22222-2-2-2-2-220000000000000000-2-22200-222-2000000000000
χ2944444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000
χ304444-4-4-4-40000000000000000000022−220022−222-22-2000000000000000000
χ314444-4-4-4-40000000000000000000022−2200−2222-22-22000000000000000000
χ324444-4-4-4-400000000000000000000−22220022−22-22-22000000000000000000
χ334444-4-4-4-400000000000000000000−222200−22222-22-2000000000000000000
χ3444-4-444-4-444-4-4-4-4444-400000000000000000000000000000000000000
χ3544-4-444-4-4-4-44444-4-44-400000000000000000000000000000000000000
χ3644-4-444-4-4-4-4-4-44444-4400000000000000000000000000000000000000
χ3744-4-4-4-4440000000000000000002i2−2i2002i2−2i2002-2-22000000000000000000
χ3844-4-4-4-4440000000000000000002i2−2i200−2i22i200-222-2000000000000000000
χ3944-4-4-4-444000000000000000000−2i22i2002i2−2i200-222-2000000000000000000
χ4044-4-4-4-444000000000000000000−2i22i200−2i22i2002-2-22000000000000000000
χ414-44-44-44-4004-4004-40000000000000000000000000000000000002i2−2i200
χ424-44-44-44-4004-4004-4000000000000000000000000000000000000−2i22i200
χ434-44-44-44-400-4400-440000004i−4i00000000000000000000000000000000
χ444-44-44-44-400-4400-44000000−4i4i00000000000000000000000000000000
χ454-44-4-44-444-4004-4000000000000000000000000000000002i2−2i200000000
χ464-44-4-44-444-4004-400000000000000000000000000000000−2i22i200000000
χ474-44-4-44-44-4400-440000004i−4i0000000000000000000000000000000000
χ484-44-4-44-44-4400-44000000−4i4i0000000000000000000000000000000000
χ494-4-444-4-44004-400-44004i−4i000000000000000000000000000000000000
χ504-4-444-4-44004-400-4400−4i4i000000000000000000000000000000000000
χ514-4-444-4-4400-44004-4000000000000000000000000000000002i2−2i2000000
χ524-4-444-4-4400-44004-400000000000000000000000000000000−2i22i2000000
χ534-4-44-444-44-400-4400000000004i−4i000000000000000000000000000000
χ544-4-44-444-44-400-440000000000−4i4i000000000000000000000000000000
χ554-4-44-444-4-44004-40000000000000000000000000000000000002i2−2i20000
χ564-4-44-444-4-44004-4000000000000000000000000000000000000−2i22i20000

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