Finite Group DatabasebetaFinite Group Databasebeta| order | 31302 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C3 |
| direct product | C37×C3⋊D141 |
| unambiguous semidirect product | C3⋊(C37×D141) |
| unambiguous semidirect product | C47⋊(C3⋊D3×C37) |
| Fitting, socle, Hall | C32×C37×C47 ⋊ C2 |
| derived, Hall | C32×C47 ⋊ C2×C37 |
| Hall | C37×C47 ⋊ C3⋊D3 |
| Hall | C32×C37 ⋊ D47 |
| Sylow | C47 ⋊ C3⋊D3×C37 |
| Sylow | C32 ⋊ C37×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C3⋊D141 |
| commutator, cosocle, hypocenter | C32×C47 | C2×C37 |
| Frattini | C1 | G |
| Fitting, socle | C32×C37×C47 | C2 |
| LCS | G ▷ C32×C47 | |
| UCS | C1 ◁ C37 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15651 |
7881 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31302, 34);