Finite Group DatabasebetaFinite Group Databasebeta| order | 35244 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×C3⋊(C3⋊#67063) |
| unambiguous semidirect product | C3⋊(C11×C3⋊#67063) |
| Fitting, socle, Hall | C32×C11×C89 ⋊ C4 |
| derived, Hall | C32×C89 ⋊ C4×C11 |
| Hall | C11×C89 ⋊ C3⋊Dic3 |
| Hall | C32×C11 ⋊ #67063 |
| Sylow | C89 ⋊ C11×C3⋊Dic3 |
| Sylow | C32 ⋊ C11×#67063 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C3⋊(C3⋊#67063) |
| commutator, hypocenter | C32×C89 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C89 | C4 |
| prime radical | C32×C11×D89 | C2 |
| cosocle | C32×D89 | C2×C11 |
| LCS | G ▷ C32×C89 | |
| UCS | C1 ◁ C11 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8811 |
2310 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35244, 105);