Finite Group DatabasebetaFinite Group Databasebeta| order | 37076 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×D23×D31 |
| unambiguous semidirect product | (C31×D23)⋊(C2×C13) |
| unambiguous semidirect product | (C23×D31)⋊(C2×C13) |
| unambiguous semidirect product | D713⋊(C2×C13) |
| Fitting, socle, Hall | C13×C23×C31 ⋊ C22 |
| derived, Hall | C23×C31 ⋊ C22×C13 |
| Hall | C13×C31 ⋊ C2×D23 |
| Hall | C13×C23 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×C13×D23 |
| Sylow | C23 ⋊ C2×C13×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D23×D31 |
| commutator, cosocle, hypocenter | C23×C31 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C23×C31 | C22 |
| LCS | G ▷ C23×C31 | |
| UCS | C1 ◁ C13 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9269 |
2873 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37076, 10);