Finite Group DatabasebetaFinite Group Databasebeta| order | 2624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊#4223 |
| unambiguous semidirect product | D41⋊(C2×C22⋊C4) |
| unambiguous semidirect product | (C2×#4223)⋊C23 |
| Fitting | C24×C41 ⋊ C4 |
| Sylow | C41 ⋊ C22×C22⋊C4 |
674 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2624, 1610);