Finite Group DatabasebetaFinite Group Databasebeta| order | 24050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C37 · Schur multiplier (H2) = C1 |
| direct product | C13×C37×D25 |
| unambiguous semidirect product | C25⋊(C2×C13×C37) |
| Fitting, Hall | C13×C25×C37 ⋊ C2 |
| derived, Sylow | C25 ⋊ C2×C13×C37 |
| Hall | C25×C37 ⋊ C2×C13 |
| Hall | C13×C25 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C37 | D25 |
| commutator, cosocle, hypocenter | C25 | C2×C13×C37 |
| Frattini | C5 | D5×C13×C37 |
| Fitting | C13×C25×C37 | C2 |
| socle | C5×C13×C37 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C13×C37 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12025 |
6734 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24050, 5);