Finite Group DatabasebetaFinite Group Databasebeta| order | 23826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#14524208 |
| Fitting, socle, derived, Hall | C11×C192 ⋊ C2×C3 |
| Hall | C11×#11762245 ⋊ C2 |
| Hall | C19×D209 ⋊ C3 |
| Hall | #11762245 ⋊ D11 |
| Sylow | C192 ⋊ C3×D11 |
| Sylow | C11 ⋊ #14524208 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C192 | C2×C3 |
| LCS | G ▷ C11×C192 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 418 |
Polycyclic presentation:
2,3,11,19^2|c^a=c^10,d^a=d^18,d^b=d^7,e^b=e^7690 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23826, 29);