Finite Group DatabasebetaFinite Group Databasebeta| order | 23769 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C139 ⋊ C9 |
| Sylow | C139 ⋊ #4296 |
| Sylow | C19 ⋊ C139⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C139 | C9 |
| prime radical, cosocle | C19⋊C3×C139 | C3 |
| LCS | G ▷ C19×C139 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2641 |
Polycyclic presentation:
3^2,19,139|a^3=b,c^a=c^4,d^a=d^96,c^b=c^7425 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23769, 9);