Finite Group DatabasebetaFinite Group Databasebeta| order | 33948 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | D41×C3⋊D69 |
| unambiguous semidirect product | (C3×D41)⋊D69 |
| unambiguous semidirect product | (C23×D41)⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C23×C41 ⋊ C22 |
| Hall | C23×C41 ⋊ C2×C3⋊D3 |
| Hall | C32×C41 ⋊ C2×D23 |
| Hall | C32×C23 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×C3⋊D69 |
| Sylow | C23 ⋊ C3⋊D3×D41 |
| Sylow | C32 ⋊ D23×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C23×C41 | C22 |
| LCS | G ▷ C32×C23×C41 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8487 |
2310 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33948, 72);