Finite Group DatabasebetaFinite Group Databasebeta| order | 31302 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×D333 |
| unambiguous semidirect product | C9⋊(C47×D37) |
| unambiguous semidirect product | C37⋊(D9×C47) |
| Fitting, Hall | C9×C37×C47 ⋊ C2 |
| derived, Hall | C9×C37 ⋊ C2×C47 |
| Hall | C37×C47 ⋊ D9 |
| Hall | C9×C47 ⋊ D37 |
| Sylow | C37 ⋊ D9×C47 |
| Sylow | C9 ⋊ C47×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | D333 |
| commutator, cosocle, hypocenter | C9×C37 | C2×C47 |
| Frattini | C3 | C47×D111 |
| Fitting | C9×C37×C47 | C2 |
| socle | C3×C37×C47 | D3 |
| LCS | G ▷ C9×C37 | |
| UCS | C1 ◁ C47 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15651 |
7896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31302, 8);