Finite Group DatabasebetaFinite Group Databasebeta| order | 37138 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D599 |
| unambiguous semidirect product | C599⋊(C2×C31) |
| Fitting, socle, Hall | C31×C599 ⋊ C2 |
| derived, Sylow | C599 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D599 |
| commutator, cosocle, hypocenter | C599 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C31×C599 | C2 |
| LCS | G ▷ C599 | |
| UCS | C1 ◁ C31 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18569 |
9331 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37138, 2);