Finite Group DatabasebetaFinite Group Databasebeta| order | 22725 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C101 · Schur multiplier (H2) = C5 |
| direct product | C101×C52⋊C9 |
| unambiguous semidirect product | C52⋊(C9×C101) |
| unambiguous semidirect product | (C52×C101)⋊C9 |
| derived, Sylow | C52 ⋊ C9×C101 |
| Hall | C52×C101 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C101 | C52⋊C3 |
| commutator, hypocenter | C52 | C9×C101 |
| Frattini | C3 | C52⋊C3×C101 |
| Fitting, socle, prime radical | C3×C52×C101 | C3 |
| cosocle | C3×C52 | C3×C101 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C101 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4545 |
3333 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22725, 8);