Finite Group DatabasebetaFinite Group Databasebeta| order | 25300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic1265 |
| unambiguous semidirect product | C23⋊(C5×Dic55) |
| derived | C5×C11×C23 ⋊ C4×C5 |
| Hall | C52×C11×C23 ⋊ C4 |
| Hall | C52×C23 ⋊ Dic11 |
| Hall | C52×C11 ⋊ Dic23 |
| Hall | C11×C23 ⋊ C5×Dic5 |
| Sylow | C52 ⋊ Dic253 |
| Sylow | C23 ⋊ C5×Dic55 |
| Sylow | C11 ⋊ C5×Dic115 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D1265 |
| commutator, hypocenter | C5×C11×C23 | C4×C5 |
| Frattini | C2 | C5×D1265 |
| Fitting, socle, prime radical | C2×C52×C11×C23 | C2 |
| cosocle | C2×C5×C11×C23 | C2×C5 |
| LCS | G ▷ C5×C11×C23 | |
| UCS | C1 ◁ C2×C5 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5060 |
6340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25300, 67);