Finite Group DatabasebetaFinite Group Databasebeta| order | 25300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×C23⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C23⋊(AGL(1,𝔽5)×C11⋊C5) |
| unambiguous semidirect product | (C11×C23⋊AGL(1,𝔽5))⋊C5 |
| Fitting, socle, derived | C5×C11×C23 ⋊ C4×C5 |
| Hall | C5×C23×C11⋊C5 ⋊ C4 |
| Hall | C5×C11⋊C5 ⋊ Dic23 |
| Hall | C11×C23 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C23 ⋊ AGL(1,𝔽5)×C11⋊C5 |
| Sylow | C11 ⋊ C5×C23⋊AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C11×C23 | C4×C5 |
| prime radical | D5×C23×C11⋊C5 | C2 |
| cosocle | D5×C11×C23 | C2×C5 |
| LCS | G ▷ C5×C11×C23 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1265 |
343 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25300, 97);