Finite Group DatabasebetaFinite Group Databasebeta| order | 22725 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C25 · Schur multiplier (H2) = C1 |
| direct product | C9×#14579005 |
| Fitting, Hall | C9×C101 ⋊ C25 |
| derived, Sylow | C101 ⋊ C9×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #14579005 |
| commutator, hypocenter | C101 | C9×C25 |
| Frattini | C3 | C3×#14579005 |
| Fitting | C9×C101 | C25 |
| socle | C3×C101 | C3×C25 |
| prime radical, cosocle | C3×C101⋊C5 | C3×C5 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C9 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 909 |
261 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22725, 6);