Finite Group DatabasebetaFinite Group Databasebeta| order | 23361 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C599⋊C13 |
| unambiguous semidirect product | C599⋊(C3×C13) |
| unambiguous semidirect product | (C3×C599)⋊C13 |
| Fitting, socle, Hall | C3×C599 ⋊ C13 |
| derived, Sylow | C599 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C599⋊C13 |
| commutator, cosocle, hypocenter | C599 | C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C599 | C13 |
| LCS | G ▷ C599 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1797 |
177 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23361, 1);