Finite Group DatabasebetaFinite Group Databasebeta| order | 25300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | (C23⋊C11)⋊#1039 |
| unambiguous semidirect product | (C23⋊#1039)⋊C11 |
| derived, Hall | C52×C23 ⋊ C4×C11 |
| Hall | C52×C23⋊C11 ⋊ C4 |
| Hall | C23⋊#1039 ⋊ C11 |
| Hall | C23⋊C11 ⋊ #1039 |
| Sylow | C52 ⋊ Dic23⋊C11 |
| Sylow | C23 ⋊ C11×#1039 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(C5⋊AGL(1,𝔽23)) |
| commutator, hypocenter | C52×C23 | C4×C11 |
| Fitting, socle, cosocle | C2×C52×C23 | C2×C11 |
| prime radical | C2×C52×C23⋊C11 | C2 |
| LCS | G ▷ C52×C23 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2300 |
Polycyclic presentation:
2,11,5^2,23,2|a^2=f,c^a=c^4,d^a=d^4,e^a=e^22,e^b=e^2358 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25300, 52);