Finite Group DatabasebetaFinite Group Databasebeta| order | 31598 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D2257 |
| unambiguous semidirect product | C37⋊(C7×D61) |
| unambiguous semidirect product | C61⋊(C7×D37) |
| Fitting, socle, Hall | C7×C37×C61 ⋊ C2 |
| derived, Hall | C37×C61 ⋊ C2×C7 |
| Hall | C7×C61 ⋊ D37 |
| Hall | C7×C37 ⋊ D61 |
| Sylow | C61 ⋊ C7×D37 |
| Sylow | C37 ⋊ C7×D61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D2257 |
| commutator, cosocle, hypocenter | C37×C61 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C37×C61 | C2 |
| LCS | G ▷ C37×C61 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15799 |
7910 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31598, 4);