Finite Group DatabasebetaFinite Group Databasebeta| order | 25308 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×Dic171 |
| unambiguous semidirect product | C9⋊(C37×Dic19) |
| unambiguous semidirect product | C19⋊(Dic9×C37) |
| derived, Hall | C9×C19 ⋊ C4×C37 |
| Hall | C9×C19×C37 ⋊ C4 |
| Hall | C19×C37 ⋊ Dic9 |
| Hall | C9×C37 ⋊ Dic19 |
| Sylow | C19 ⋊ Dic9×C37 |
| Sylow | C9 ⋊ C37×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | D171 |
| commutator, hypocenter | C9×C19 | C4×C37 |
| Frattini | C2×C3 | C37×D57 |
| Fitting | C2×C9×C19×C37 | C2 |
| socle | C2×C3×C19×C37 | D3 |
| LCS | G ▷ C9×C19 | |
| UCS | C1 ◁ C2×C37 | |
36 conjugacy classes of subgroups.
6438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25308, 11);