Finite Group DatabasebetaFinite Group Databasebeta| order | 25300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×Dic253 |
| unambiguous semidirect product | C23⋊(C25×Dic11) |
| derived, Hall | C11×C23 ⋊ C4×C25 |
| Hall | C11×C23×C25 ⋊ C4 |
| Hall | C23×C25 ⋊ Dic11 |
| Hall | C11×C25 ⋊ Dic23 |
| Sylow | C23 ⋊ C25×Dic11 |
| Sylow | C11 ⋊ C25×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C25 | D253 |
| commutator, hypocenter | C11×C23 | C4×C25 |
| Frattini | C2×C5 | C5×D253 |
| Fitting | C2×C11×C23×C25 | C2 |
| socle, prime radical, cosocle | C2×C5×C11×C23 | C2×C5 |
| LCS | G ▷ C11×C23 | |
| UCS | C1 ◁ C2×C25 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25300 |
6400 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25300, 6);