Finite Group DatabasebetaFinite Group Databasebeta| order | 24525 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C52⋊#11758281 |
| Fitting, socle, derived, Hall | C52×C109 ⋊ C9 |
| Sylow | C109 ⋊ C52⋊C9 |
| Sylow | C52 ⋊ #11758281 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C109 | C9 |
| prime radical, cosocle | C52×C109⋊C3 | C3 |
| LCS | G ▷ C52×C109 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1635 |
Polycyclic presentation:
3^2,5^2,109|a^3=b,c^a=cd^2,d^a=cd^3,e^a=e^16,e^b=e^63333 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24525, 11);