Finite Group DatabasebetaFinite Group Databasebeta| order | 25300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C11⋊(C23⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C23⋊(C5×C11⋊AGL(1,𝔽5)) |
| Fitting, socle, Hall | C52×C11×C23 ⋊ C4 |
| derived | C5×C11×C23 ⋊ C4×C5 |
| Hall | C52×C23 ⋊ Dic11 |
| Hall | C52×C11 ⋊ Dic23 |
| Hall | C11×C23 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C52 ⋊ Dic253 |
| Sylow | C23 ⋊ C5×C11⋊AGL(1,𝔽5) |
| Sylow | C11 ⋊ C5×C23⋊AGL(1,𝔽5) |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5060 |
2545 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25300, 123);