Finite Group DatabasebetaFinite Group Databasebeta| order | 37596 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C3⋊#11757210 |
| unambiguous semidirect product | C3⋊(C13×#11757210) |
| Fitting, socle, Hall | C3×C13×C241 ⋊ C4 |
| derived, Hall | C3×C241 ⋊ C4×C13 |
| Hall | C13×C241 ⋊ Dic3 |
| Sylow | C241 ⋊ Dic3×C13 |
| Hall | C3×C13 ⋊ #11757210 |
| Sylow | C3 ⋊ C13×#11757210 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C3⋊#11757210 |
| commutator, hypocenter | C3×C241 | C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C241 | C4 |
| prime radical | C3×C13×D241 | C2 |
| cosocle | C3×D241 | C2×C13 |
| LCS | G ▷ C3×C241 | |
| UCS | C1 ◁ C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9399 |
2418 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37596, 73);