Finite Group DatabasebetaFinite Group Databasebeta| order | 24525 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C9 · Schur multiplier (H2) = C5 |
| direct product | C52×#11758281 |
| Fitting, socle, Hall | C52×C109 ⋊ C9 |
| derived, Sylow | C109 ⋊ C52×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | #11758281 |
| commutator, hypocenter | C109 | C52×C9 |
| Frattini | C1 | G |
| Fitting, socle | C52×C109 | C9 |
| prime radical | C52×C109⋊C3 | C3 |
| cosocle | C109⋊C3 | C3×C52 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C52 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2725 |
525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24525, 13);