Finite Group DatabasebetaFinite Group Databasebeta| order | 22725 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C25 · Schur multiplier (H2) = C1 |
| direct product | C9×#14579003 |
| derived, Sylow | C101 ⋊ C9×C25 |
| Hall | C9×C101 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C9 | C101⋊C5 |
| commutator, hypocenter | C101 | C9×C25 |
| Frattini | C3×C5 | C3×C101⋊C5 |
| Fitting | C5×C9×C101 | C5 |
| socle, prime radical, cosocle | C3×C5×C101 | C3×C5 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C5×C9 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22725 |
1125 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22725, 2);