Finite Group DatabasebetaFinite Group Databasebeta| order | 31450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D629 |
| unambiguous semidirect product | C17⋊(C52×D37) |
| unambiguous semidirect product | C37⋊(C52×D17) |
| Fitting, socle, Hall | C52×C17×C37 ⋊ C2 |
| derived, Hall | C17×C37 ⋊ C2×C52 |
| Hall | C52×C37 ⋊ D17 |
| Hall | C52×C17 ⋊ D37 |
| Sylow | C37 ⋊ C52×D17 |
| Sylow | C17 ⋊ C52×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D629 |
| commutator, cosocle, hypocenter | C17×C37 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17×C37 | C2 |
| LCS | G ▷ C17×C37 | |
| UCS | C1 ◁ C52 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15725 |
7900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31450, 12);