Finite Group DatabasebetaFinite Group Databasebeta| order | 25300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | (C23⋊C11)⋊#1044 |
| unambiguous semidirect product | (C23⋊#1044)⋊C11 |
| Fitting, socle, derived, Hall | C52×C23 ⋊ C4×C11 |
| Hall | C52×C23⋊C11 ⋊ C4 |
| Hall | C23⋊#1044 ⋊ C11 |
| Hall | C23⋊C11 ⋊ #1044 |
| Sylow | C52 ⋊ Dic23⋊C11 |
| Sylow | C23 ⋊ C11×#1044 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C23 | C4×C11 |
| prime radical | C5⋊D5×C23⋊C11 | C2 |
| cosocle | C23×C5⋊D5 | C2×C11 |
| LCS | G ▷ C52×C23 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 230 |
Polycyclic presentation:
2,11,2,5^2,23|a^2=c,d^a=d^2,e^a=e^3,f^a=f^22,f^b=f^2,d^c=d^4,e^c=e^4124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25300, 86);