Finite Group DatabasebetaFinite Group Databasebeta| order | 25300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | #1035×C23⋊C11 |
| unambiguous semidirect product | (C23×#1035)⋊C11 |
| Fitting, derived, Hall | C23×C25 ⋊ C4×C11 |
| Hall | C25×C23⋊C11 ⋊ C4 |
| Hall | C23×#1035 ⋊ C11 |
| Sylow | C25 ⋊ C4×C23⋊C11 |
| Sylow | C23 ⋊ C11×#1035 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C23×C25 | C4×C11 |
| Frattini | C5 | AGL(1,𝔽5)×C23⋊C11 |
| socle | C5×C23 | C11×AGL(1,𝔽5) |
| prime radical | D25×C23⋊C11 | C2 |
| cosocle | C23×D25 | C2×C11 |
| LCS | G ▷ C23×C25 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 575 |
130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25300, 19);