Finite Group DatabasebetaFinite Group Databasebeta| order | 23049 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C197 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C9×C197 |
| unambiguous semidirect product | C13⋊(C9×C197) |
| unambiguous semidirect product | (C13×C197)⋊C9 |
| derived, Sylow | C13 ⋊ C9×C197 |
| Hall | C13×C197 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C197 | C13⋊C3 |
| commutator, hypocenter | C13 | C9×C197 |
| Frattini | C3 | C13⋊C3×C197 |
| Fitting, socle, prime radical | C3×C13×C197 | C3 |
| cosocle | C3×C13 | C3×C197 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C197 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23049 |
4137 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23049, 2);