Finite Group Databasebeta

← Group #104591

Character table — Group #104591

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111111112222444444444488888888816161616161616161616161616161616161616163232
order12222222444444444444444888888884444444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ9222222222222222-2-2-2-2-2-22-22222-2-2-2-20000000000000000000000
χ10222222222222222-2-2-2-2-2-22-2-2-2-2-222220000000000000000000000
χ11222222222222-2-2-222-2-222-2-20000000000000000000022-2-2000000
χ12222222222222-2-2-222-2-222-2-200000000000000000000-2-222000000
χ13222222222222-2-2-2-2-222-2-2-2200000000000000000000000022-2-200
χ14222222222222-2-2-2-2-222-2-2-22000000000000000000000000-2-22200
χ1522222222-2-2-2-222-222-2-2-2-2-2200000000000000002i2i−2i−2i0000000000
χ1622222222-2-2-2-222-222-2-2-2-2-220000000000000000−2i−2i2i2i0000000000
χ1722222222-2-2-2-222-2-2-22222-2-20000000022-2-2000000000000000000
χ1822222222-2-2-2-222-2-2-22222-2-200000000-2-222000000000000000000
χ1922222222-2-2-2-2-2-222222-2-22-200000000000000000000000000002-2
χ2022222222-2-2-2-2-2-222222-2-22-20000000000000000000000000000-22
χ2122222222-2-2-2-2-2-22-2-2-2-2222200000000000022-2-200000000000000
χ2222222222-2-2-2-2-2-22-2-2-2-22222000000000000-2-22200000000000000
χ2322-2-2-2-22222-2-20002-2002-20022−2−222−2−2000000000000002i−2ii2−i2i2−i200
χ2422-2-2-2-22222-2-20002-2002-20022−2−222−2−200000000000000−2i2i−i2i2−i2i200
χ2522-2-2-2-22222-2-20002-2002-200−2−222−2−222000000000000002i−2i−i2i2−i2i200
χ2622-2-2-2-22222-2-20002-2002-200−2−222−2−22200000000000000−2i2ii2−i2i2−i200
χ2722-2-2-2-22222-2-2000-2200-220022−2−2−2−2220000000000002i−2i00i2−i2−i2i200
χ2822-2-2-2-22222-2-2000-2200-220022−2−2−2−222000000000000−2i2i00−i2i2i2−i200
χ2922-2-2-2-22222-2-2000-2200-2200−2−22222−2−20000000000002i−2i00−i2i2i2−i200
χ3022-2-2-2-22222-2-2000-2200-2200−2−22222−2−2000000000000−2i2i00i2−i2−i2i200
χ31444-44-4-4-40000000004-400002-22-22-22-20000000000000000000000
χ32444-44-4-4-40000000004-40000-22-22-22-220000000000000000000000
χ33444-44-4-4-4000000000-4400002-22-2-22-220000000000000000000000
χ34444-44-4-4-4000000000-440000-22-222-22-20000000000000000000000
χ3544-44-44-4-400004-4000000000000022−22−22220000000000000000000000
χ3644-44-44-4-400004-40000000000000−222222−220000000000000000000000
χ3744-44-44-4-40000-4400000000022−22−222200000000000000000000000000
χ3844-44-44-4-40000-44000000000−222222−2200000000000000000000000000
χ3944-4-4-4-444-4-4440004-400-4400000000000000000000000000000000
χ4044-4-4-4-444-4-444000-44004-400000000000000000000000000000000
χ414-444-4-44-40000004000000-4000000000000000002-22-20000000000
χ424-444-4-44-40000004000000-400000000000000000-22-220000000000
χ434-444-4-44-4000000-40000004000000000000000002i−2i−2i2i0000000000
χ444-444-4-44-4000000-4000000400000000000000000−2i2i2i−2i0000000000
χ454-44-4-44-444i−4i4i−4i000000000000000000000002i−2i2-200000000000000
χ464-44-4-44-444i−4i4i−4i00000000000000000000000−2i2i-2200000000000000
χ474-44-4-44-44−4i4i−4i4i000000000000000000000002i−2i-2200000000000000
χ484-44-4-44-44−4i4i−4i4i00000000000000000000000−2i2i2-200000000000000
χ494-4-444-4-444i−4i−4i4i00000000000000000002-22i−2i000000000000000000
χ504-4-444-4-444i−4i−4i4i0000000000000000000-22−2i2i000000000000000000
χ514-4-444-4-44−4i4i4i−4i00000000000000000002-2−2i2i000000000000000000
χ524-4-444-4-44−4i4i4i−4i0000000000000000000-222i−2i000000000000000000
χ538-8-8-8888-8000000000000000000000000000000000000000000000

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