Finite Group DatabasebetaFinite Group Databasebeta| order | 25452 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic909 |
| unambiguous semidirect product | C9⋊(C7×Dic101) |
| derived, Hall | C9×C101 ⋊ C4×C7 |
| Hall | C7×C9×C101 ⋊ C4 |
| Hall | C7×C101 ⋊ Dic9 |
| Sylow | C101 ⋊ C7×Dic9 |
| Hall | C7×C9 ⋊ Dic101 |
| Sylow | C9 ⋊ C7×Dic101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D909 |
| commutator, hypocenter | C9×C101 | C4×C7 |
| Frattini | C2×C3 | C7×D303 |
| Fitting | C2×C7×C9×C101 | C2 |
| socle, prime radical | C2×C3×C7×C101 | D3 |
| cosocle | C2×C9×C101 | C2×C7 |
| LCS | G ▷ C9×C101 | |
| UCS | C1 ◁ C2×C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25452 |
6384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25452, 7);