Finite Group DatabasebetaFinite Group Databasebeta| order | 31450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C37 · Schur multiplier (H2) = C1 |
| direct product | C5×C37×D85 |
| unambiguous semidirect product | C5⋊(C5×D17×C37) |
| unambiguous semidirect product | C17⋊(C5×D5×C37) |
| Fitting, socle, Hall | C52×C17×C37 ⋊ C2 |
| derived | C5×C17 ⋊ C2×C5×C37 |
| Hall | C52×C37 ⋊ D17 |
| Hall | C17×C37 ⋊ C5×D5 |
| Hall | C52×C17 ⋊ C2×C37 |
| Sylow | C52 ⋊ D17×C37 |
| Sylow | C17 ⋊ C5×D5×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C37 | D85 |
| commutator, cosocle, hypocenter | C5×C17 | C2×C5×C37 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17×C37 | C2 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C5×C37 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6290 |
8140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31450, 15);