Finite Group DatabasebetaFinite Group Databasebeta| order | 36556 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×C19⋊#261 |
| unambiguous semidirect product | C19⋊(C37×#261) |
| Fitting, socle, Hall | C13×C19×C37 ⋊ C4 |
| derived, Hall | C13×C19 ⋊ C4×C37 |
| Hall | C19×C37 ⋊ #261 |
| Hall | C13×C37 ⋊ Dic19 |
| Sylow | C19 ⋊ C37×#261 |
| Sylow | C13 ⋊ C37×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C19⋊#261 |
| commutator, hypocenter | C13×C19 | C4×C37 |
| Frattini | C1 | G |
| Fitting, socle | C13×C19×C37 | C4 |
| prime radical | C19×D13×C37 | C2 |
| cosocle | C19×D13 | C2×C37 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C37 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9139 |
2923 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36556, 17);