Finite Group Databasebeta

← Group #173609

Character table — Group #173609

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222444444444444444444444444422444488888888888822
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11-1-1-1-11-11-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-11-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-111111-1-1-1-1-1-1-111-11111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1-1-1-1-111111-11-1-1-111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-111111-11-1-1-11-1-1-1-111111111-1-1
χ91111111111-1-1-1-11-1-111111-1-111-1-1-111-1-111-11-1-111-1-111-1-111-1-11-1
χ101111111111-1-1-1-11-1-111111-1-111-1-1-111-1-111-11-1-1-1-111-1-111-1-111-11
χ111111111111-1-1-1-11-1-111111-1-1-1-111-1-1-1111-1-1-11111-1-111-1-1-1-111-11
χ121111111111-1-1-1-11-1-111111-1-1-1-111-1-1-1111-1-1-111-1-111-1-11111-1-11-1
χ131111111111-1-1-1-11-1-1111-1-11111-1-1-1-1-111-1-111-1111-1-1-1-11111-1-1-11
χ141111111111-1-1-1-11-1-1111-1-11111-1-1-1-1-111-1-111-11-1-11111-1-1-1-1111-1
χ151111111111-1-1-1-11-1-1111-1-111-1-111-111-1-1-111-11-111-1-1-1-111-1-1111-1
χ161111111111-1-1-1-11-1-1111-1-111-1-111-111-1-1-111-11-1-1-11111-1-111-1-1-11
χ17222222222-222-2-2-2222-2-200002222-20000000-2-2000000000000000
χ18222222222-222-2-2-2222-2-20000-2-2-2-2-2000000022000000000000000
χ19222222222-2-2-222-2-2-22-2-2000022-2-220000000-22000000000000000
χ20222222222-2-2-222-2-2-22-2-20000-2-222200000002-2000000000000000
χ2122222222-2222-2-2-2-2-2-22-222-2-2000020000-20200000000000000000
χ2222222222-2222-2-2-2-2-2-22-2-2-22200002000020-200000000000000000
χ2322222222-22-2-222-222-22-222220000-20000-20-200000000000000000
χ2422222222-22-2-222-222-22-2-2-2-2-20000-2000020200000000000000000
χ2522222222-2-222222-2-2-2-2200000000-222220-2000-200000000000000
χ2622222222-2-222222-2-2-2-2200000000-2-2-2-2-202000200000000000000
χ2722222222-2-2-2-2-2-2222-2-2200000000222-2-20-2000200000000000000
χ2822222222-2-2-2-2-2-2222-2-22000000002-2-22202000-200000000000000
χ29222-2-22-2-2002-22-220000-20000000002i−2i2i−2i0000000000i2−i2i2−i22−22−200
χ30222-2-22-2-2002-22-220000-20000000002i−2i2i−2i0000000000−i2i2−i2i2−22−2200
χ31222-2-22-2-2002-22-220000-2000000000−2i2i−2i2i0000000000i2−i2i2−i2−22−2200
χ32222-2-22-2-2002-22-220000-2000000000−2i2i−2i2i0000000000−i2i2−i2i22−22−200
χ33222-2-22-2-200-22-2220000-20000000002i−2i−2i2i0000000000i2−i2−i2i22−2−2200
χ34222-2-22-2-200-22-2220000-20000000002i−2i−2i2i0000000000−i2i2i2−i2−222−200
χ35222-2-22-2-200-22-2220000-2000000000−2i2i2i−2i0000000000i2−i2−i2i2−222−200
χ36222-2-22-2-200-22-2220000-2000000000−2i2i2i−2i0000000000−i2i2i2−i22−2−2200
χ37444-4-44-4-4004-4-44-400004000000000000000000000000000000000
χ38444-4-44-4-400-444-4-400004000000000000000000000000000000000
χ3944-44-4-44-40400000000-404i−4i0000000000000000000000000000000
χ4044-44-4-44-40400000000-40−4i4i0000000000000000000000000000000
χ4144-44-4-44-40-40000000040004-400000000000000000000000000000
χ4244-44-4-44-40-4000000004000-4400000000000000000000000000000
χ434-44-44-44-4400000000-4000000004i−4i0000000000000000000000000
χ444-44-44-44-4400000000-400000000−4i4i0000000000000000000000000
χ454-44-44-44-4-40000000040000004-4000000000000000000000000000
χ464-44-44-44-4-4000000004000000-44000000000000000000000000000
χ474-4-4-4-444400000004-400000000000000000000002-22-20000000000
χ484-4-4-4-444400000004-40000000000000000000000-22-220000000000
χ494-4-4-4-44440000000-4400000000000000000000002-2-220000000000
χ504-4-4-4-44440000000-440000000000000000000000-222-20000000000
χ5188-8-88-8-88000000000000000000000000000000000000000000000
χ528-888-8-8-88000000000000000000000000000000000000000000000
χ538-8-8888-8-8000000000000000000000000000000000000000000000

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