Finite Group DatabasebetaFinite Group Databasebeta| order | 37076 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×C31⋊#261 |
| unambiguous semidirect product | C31⋊(C23×#261) |
| Fitting, socle, Hall | C13×C23×C31 ⋊ C4 |
| derived, Hall | C13×C31 ⋊ C4×C23 |
| Hall | C23×C31 ⋊ #261 |
| Hall | C13×C23 ⋊ Dic31 |
| Sylow | C31 ⋊ C23×#261 |
| Sylow | C13 ⋊ C23×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C31⋊#261 |
| commutator, hypocenter | C13×C31 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C13×C23×C31 | C4 |
| prime radical | C23×D13×C31 | C2 |
| cosocle | D13×C31 | C2×C23 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9269 |
2921 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37076, 12);