Finite Group DatabasebetaFinite Group Databasebeta| order | 26607 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×C181⋊C3 |
| unambiguous semidirect product | C181⋊(C3×C49) |
| Fitting, Hall | C49×C181 ⋊ C3 |
| derived, Sylow | C181 ⋊ C3×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | C181⋊C3 |
| commutator, hypocenter | C181 | C3×C49 |
| Frattini | C7 | C7×C181⋊C3 |
| Fitting | C49×C181 | C3 |
| socle, cosocle | C7×C181 | C3×C7 |
| prime radical | C7×C181⋊C3 | C7 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C49 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8869 |
3087 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26607, 3);