Finite Group DatabasebetaFinite Group Databasebeta| order | 24050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C5 |
| direct product | C37×C5⋊D65 |
| unambiguous semidirect product | C5⋊(C37×D65) |
| unambiguous semidirect product | C13⋊(C37×C5⋊D5) |
| Fitting, socle, Hall | C52×C13×C37 ⋊ C2 |
| derived, Hall | C52×C13 ⋊ C2×C37 |
| Hall | C52×C37 ⋊ D13 |
| Hall | C13×C37 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D13×C37 |
| Sylow | C13 ⋊ C37×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C5⋊D65 |
| commutator, cosocle, hypocenter | C52×C13 | C2×C37 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13×C37 | C2 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 ◁ C37 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12025 |
6068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24050, 19);