Finite Group DatabasebetaFinite Group Databasebeta| order | 25300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊((C11⋊C5)⋊Dic5) |
| unambiguous semidirect product | (C11⋊C5)⋊Dic115 |
| unambiguous semidirect product | Dic1265⋊C5 |
| derived | C5×C11×C23 ⋊ C4×C5 |
| Hall | C5×C23×C11⋊C5 ⋊ C4 |
| Hall | C5×C11⋊C5 ⋊ Dic23 |
| Hall | C11×C23 ⋊ C5×Dic5 |
| Sylow | C23 ⋊ (C11⋊C5)⋊Dic5 |
| Sylow | C11 ⋊ C5×Dic115 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(C23⋊AGL(1,𝔽11)) |
| commutator, hypocenter | C5×C11×C23 | C4×C5 |
| Fitting, socle, cosocle | C2×C5×C11×C23 | C2×C5 |
| prime radical | C2×C5×C23×C11⋊C5 | C2 |
| LCS | G ▷ C5×C11×C23 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5060 |
Polycyclic presentation:
2,5^2,11,23,2|a^2=f,c^a=c^4,d^a=d^10,e^a=e^22,d^b=d^4820 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25300, 59);