Finite Group DatabasebetaFinite Group Databasebeta| order | 24700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×C19⋊#261 |
| unambiguous semidirect product | C19⋊(C52×#261) |
| Fitting, socle, Hall | C52×C13×C19 ⋊ C4 |
| derived, Hall | C13×C19 ⋊ C4×C52 |
| Hall | C52×C19 ⋊ #261 |
| Hall | C52×C13 ⋊ Dic19 |
| Sylow | C19 ⋊ C52×#261 |
| Sylow | C13 ⋊ C52×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C19⋊#261 |
| commutator, hypocenter | C13×C19 | C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13×C19 | C4 |
| prime radical | C52×C19×D13 | C2 |
| cosocle | C19×D13 | C2×C52 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C52 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6175 |
1975 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24700, 50);