Finite Group DatabasebetaFinite Group Databasebeta| order | 14300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×(C11⋊C5)⋊#261 |
| unambiguous semidirect product | (C11⋊C5)⋊(C5×#261) |
| unambiguous semidirect product | (C11⋊#261)⋊C52 |
| unambiguous semidirect product | (C5×C11⋊#261)⋊C5 |
| Fitting, socle | C5×C11×C13 ⋊ C4×C5 |
| derived, Hall | C11×C13 ⋊ C4×C52 |
| Hall | C5×C13×C11⋊C5 ⋊ C4 |
| Hall | C11⋊#261 ⋊ C52 |
| Hall | C5×C11⋊C5 ⋊ #261 |
| Sylow | C13 ⋊ C5×Dic11⋊C5 |
| Sylow | C11 ⋊ C52×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | (C11⋊C5)⋊#261 |
| commutator, hypocenter | C11×C13 | C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C13 | C4×C5 |
| prime radical | C5×D13×C11⋊C5 | C2 |
| cosocle | C11×D13 | C2×C52 |
| LCS | G ▷ C11×C13 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 715 |
215 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14300, 68);