Finite Group DatabasebetaFinite Group Databasebeta| order | 36556 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D37×D247 |
| unambiguous semidirect product | (C13×D37)⋊D19 |
| unambiguous semidirect product | (C19×D37)⋊D13 |
| Fitting, socle, derived, Hall | C13×C19×C37 ⋊ C22 |
| Hall | C19×C37 ⋊ C2×D13 |
| Hall | C13×C37 ⋊ C2×D19 |
| Hall | C13×C19 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×D247 |
| Sylow | C19 ⋊ D13×D37 |
| Sylow | C13 ⋊ D19×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C19×C37 | C22 |
| LCS | G ▷ C13×C19×C37 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9139 |
2500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36556, 24);