Finite Group DatabasebetaFinite Group Databasebeta| order | 2624 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C4×#4223 |
| unambiguous semidirect product | D41⋊(C2×C42) |
| Fitting | C22×C4×C41 ⋊ C4 |
| derived, Sylow | C41 ⋊ C22×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #4223 |
| commutator, hypocenter | C41 | C22×C42 |
| Frattini | C2 | C23×#4223 |
| Fitting | C22×C4×C41 | C4 |
| socle | C23×C41 | C2×C4 |
| prime radical | C23×D41 | C22 |
| cosocle | C2×D41 | C24 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C22×C4 | |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2624, 1609);