Finite Group Databasebeta

← Group #104609

Character table — Group #104609

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111111112222444444444488888888816161616161616161616161616161616161616163232
order12222222444444444444444888888882244444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
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
χ611111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ922222222222222-2-2-222-2-2-2-20000000000000000000022-2-2000000
χ1022222222222222-2-2-222-2-2-2-200000000000000000000-2-222000000
χ11222222222222-2-2222-2-2-2-22-22222-2-2-2-20000000000000000000000
χ12222222222222-2-2222-2-2-2-22-2-2-2-2-222220000000000000000000000
χ13222222222222-2-2-2-2-2-2-222-2200000000000000000000000022-2-200
χ14222222222222-2-2-2-2-2-2-222-22000000000000000000000000-2-22200
χ1522222222-2-2-2-2222-2-2-2-2222-200000000000000000000000000002-2
χ1622222222-2-2-2-2222-2-2-2-2222-20000000000000000000000000000-22
χ1722222222-2-2-2-222-222-2-2-2-2-2200000000000000002i2i−2i−2i0000000000
χ1822222222-2-2-2-222-222-2-2-2-2-220000000000000000−2i−2i2i2i0000000000
χ1922222222-2-2-2-2-2-22-2-222-2-2220000000022-2-2000000000000000000
χ2022222222-2-2-2-2-2-22-2-222-2-22200000000-2-222000000000000000000
χ2122222222-2-2-2-2-2-2-2222222-2-200000000000022-2-200000000000000
χ2222222222-2-2-2-2-2-2-2222222-2-2000000000000-2-22200000000000000
χ23222-22-2-2-2-2-2222-20002-20000i2i2−i2−i2i2i2−i2−i2000000000000002i−2i2−22−200
χ24222-22-2-2-2-2-2222-20002-20000i2i2−i2−i2i2i2−i2−i200000000000000−2i2i−22−2200
χ25222-22-2-2-2-2-2222-20002-20000−i2−i2i2i2−i2−i2i2i2000000000000002i−2i−22−2200
χ26222-22-2-2-2-2-2222-20002-20000−i2−i2i2i2−i2−i2i2i200000000000000−2i2i2−22−200
χ27222-22-2-2-2-2-222-22000-220000i2i2−i2−i2−i2−i2i2i20000000000002i−2i002−2−2200
χ28222-22-2-2-2-2-222-22000-220000i2i2−i2−i2−i2−i2i2i2000000000000−2i2i00−222−200
χ29222-22-2-2-2-2-222-22000-220000−i2−i2i2i2i2i2−i2−i20000000000002i−2i00−222−200
χ30222-22-2-2-2-2-222-22000-220000−i2−i2i2i2i2i2−i2−i2000000000000−2i2i002−2−2200
χ31444-44-4-4-444-4-44-4000-440000000000000000000000000000000000
χ32444-44-4-4-444-4-4-440004-40000000000000000000000000000000000
χ3344-44-4-4-444i−4i4i−4i000000000000000000000002i−2i2-200000000000000
χ3444-44-4-4-444i−4i4i−4i00000000000000000000000−2i2i-2200000000000000
χ3544-44-4-4-44−4i4i−4i4i000000000000000000000002i−2i-2200000000000000
χ3644-44-4-4-44−4i4i−4i4i00000000000000000000000−2i2i2-200000000000000
χ3744-4-4-444-44i−4i−4i4i00000000000000000002-22i−2i000000000000000000
χ3844-4-4-444-44i−4i−4i4i0000000000000000000-22−2i2i000000000000000000
χ3944-4-4-444-4−4i4i4i−4i00000000000000000002-2−2i2i000000000000000000
χ4044-4-4-444-4−4i4i4i−4i0000000000000000000-222i−2i000000000000000000
χ414-44-4-44-440000004000000-4000000000000000002i−2i2i−2i0000000000
χ424-44-4-44-440000004000000-400000000000000000−2i2i−2i2i0000000000
χ434-44-4-44-44000000-40000004000000000000000002-2-220000000000
χ444-44-4-44-44000000-4000000400000000000000000-222-20000000000
χ454-4-4444-4-4000000000004-4002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ464-4-4444-4-4000000000004-400−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ474-4-4444-4-400000000000-44002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ484-4-4444-4-400000000000-4400−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ494-4-4-44-44400000004-4000000000022−22−22220000000000000000000000
χ504-4-4-44-44400000004-40000000000−222222−220000000000000000000000
χ514-4-4-44-4440000000-4400000022−22−222200000000000000000000000000
χ524-4-4-44-4440000000-44000000−222222−2200000000000000000000000000
χ538-888-8-88-8000000000000000000000000000000000000000000000

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