Finite Group Databasebeta

← Group #340412

Character table — Group #340412

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111111112222222244888888888888888816161616161616161616161616161616323232
order12222222444444444444448888888888882444444488888888244
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-111-1-1-1-111-11111-1-1-1-1-111-1-1-1-11
χ31111111111111111111111-1-11111-1-1-1-1-1-1-111111-1111-1-1-1-1-1-11-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-11111-11-1111-1-1-1-111-1-111-11-1
χ511111111111111111111-1-11111111111111-1-11-1-11-11111-1-1-1-1-1-1-1
χ611111111111111111111-1-111-1-1-1-111-1-1-1-11-111-1-111-1-1-1-1-1-11111-1
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11111-111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11-1-11111-1-11-11
χ9111111111111111111-1-111111111111111-111-1-1-1-11-1-1-1-11111-1-1-1
χ10111111111111111111-1-11111-1-1-1-111-1-1-1-1-11-1-1-1-1-1-1111111-1-111-1
χ11111111111111111111-1-111-1-11111-1-1-1-1-1-1111-1-1-111-1-111-1-1-1-1-111
χ12111111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-111-1-1-1-1111-11
χ13111111111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111
χ14111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11-111-111111-1-111-1-11
χ15111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1-1111-1-1-11111111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1111111-1-111-1-1-11-1
χ172222222222-2-22-2-22-2-22200220000-2-20000200-200-2000000000000
χ182222222222-2-22-2-22-2-22200-2-20000220000-200-2002000000000000
χ192222222222-2-22-2-22-2-2-2-200220000-2-20000-2002002000000000000
χ202222222222-2-22-2-22-2-2-2-200-2-20000220000200200-2000000000000
χ2122222222-2-222-222-2-2-200220022-2-20000000-220000-200000000000
χ2222222222-2-222-222-2-2-2002200-2-2220000000-2-20000200000000000
χ2322222222-2-222-222-2-2-200-2-20022-2-200000002-20000200000000000
χ2422222222-2-222-222-2-2-200-2-200-2-2220000000220000-200000000000
χ2522-2-22-2-22-2-2-2-222222-2000000000000000000002-200002-2002-2000
χ2622-2-22-2-22-2-2-2-222222-2000000000000000000002-20000-2200-22000
χ2722-2-22-2-22-2-2-2-222222-200000000000000000000-2200002-200-22000
χ2822-2-22-2-22-2-2-2-222222-200000000000000000000-220000-22002-2000
χ2944444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000
χ30444-4-44-4-44-400400-40000004-400000000000000000000000000000
χ31444-4-44-4-44-400400-4000000-4400000000000000000000000000000
χ32444-4-44-4-4-4400-4004000000000000002i22i2−2i2−2i20000000000000000000
χ33444-4-44-4-4-4400-400400000000000000−2i2−2i22i22i20000000000000000000
χ3444-44-4-44-44-400-4004004i−4i000000000000000000000000000000000
χ3544-44-4-44-44-400-400400−4i4i000000000000000000000000000000000
χ3644-44-4-44-4-4400400-40000000000000000000000000022−22000000000
χ3744-44-4-44-4-4400400-400000000000000000000000000−2222000000000
χ3844-4-44-4-444444-4-4-4-44-400000000000000000000000000000000000
χ3944-4-44-4-4444-4-4-444-4-4400000000000000000000000000000000000
χ4044-4-44-4-44-4-4444-4-44-4400000000000000000000000000000000000
χ414-44-4-4-444004-404-4000000000000000000000000000000022−2200000
χ424-44-4-4-444004-404-40000000000000000000000000000000−222200000
χ434-44-4-4-44400-440-44000004-40000000000000000000000000000000
χ444-44-4-4-44400-440-4400000-440000000000000000000000000000000
χ454-4-44-44-44004-40-4400000000000000022−2222−220000000000000000000
χ464-4-44-44-44004-40-44000000000000000−2222−22220000000000000000000
χ474-4-44-44-4400-4404-40000000004-4000000000000000000000000000
χ484-4-44-44-4400-4404-4000000000-44000000000000000000000000000
χ494-4-4-4444-40000000000000000002i2−2i222−222i−2i−2i2i0000000000000000000
χ504-4-4-4444-40000000000000000002i2−2i2−2222−2i2i2i−2i0000000000000000000
χ514-4-4-4444-4000000000000000000−2i22i222−22−2i2i2i−2i0000000000000000000
χ524-4-4-4444-4000000000000000000−2i22i2−22222i−2i−2i2i0000000000000000000
χ538-8888-8-8-8000000000000000000000000000000000000000000000

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