Finite Group DatabasebetaFinite Group Databasebeta| order | 24525 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#11758281 |
| Fitting, Hall | C25×C109 ⋊ C9 |
| derived, Sylow | C109 ⋊ C9×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #11758281 |
| commutator, hypocenter | C109 | C9×C25 |
| Frattini | C5 | C5×#11758281 |
| Fitting | C25×C109 | C9 |
| socle | C5×C109 | C5×C9 |
| prime radical, cosocle | C5×C109⋊C3 | C3×C5 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C25 | |
18 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, 4);