Finite Group DatabasebetaFinite Group Databasebeta| order | 33948 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×D23×D41 |
| unambiguous semidirect product | (C41×D23)⋊(C2×C9) |
| unambiguous semidirect product | (C23×D41)⋊(C2×C9) |
| unambiguous semidirect product | D943⋊(C2×C9) |
| Fitting, Hall | C9×C23×C41 ⋊ C22 |
| derived, Hall | C23×C41 ⋊ C22×C9 |
| Hall | C9×C41 ⋊ C2×D23 |
| Hall | C9×C23 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×C9×D23 |
| Sylow | C23 ⋊ C2×C9×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D23×D41 |
| commutator, hypocenter | C23×C41 | C22×C9 |
| Frattini | C3 | C3×D23×D41 |
| Fitting | C9×C23×C41 | C22 |
| socle, cosocle | C3×C23×C41 | C22×C3 |
| prime radical | C3×D23×D41 | C3 |
| LCS | G ▷ C23×C41 | |
| UCS | C1 ◁ C9 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8487 |
2574 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33948, 12);