Finite Group DatabasebetaFinite Group Databasebeta| order | 25074 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×#13184226⋊C2 |
| unambiguous semidirect product | #13184226⋊(C2×C7) |
| Fitting, socle, Hall | C7×C199 ⋊ C2×C9 |
| derived, Sylow | C199 ⋊ C2×C7×C9 |
| Hall | C7×#13184226 ⋊ C2 |
| Hall | C7×D199 ⋊ C9 |
| Hall | #13184226 ⋊ C2×C7 |
| Hall | D199 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #13184226⋊C2 |
| commutator, hypocenter | C199 | C2×C7×C9 |
| Frattini | C1 | G |
| Fitting, socle | C7×C199 | C2×C9 |
| prime radical | C7×D199⋊C3 | C3 |
| cosocle | C199⋊C3 | C2×C3×C7 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1393 |
203 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25074, 26);