Finite Group DatabasebetaFinite Group Databasebeta| order | 23180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊(#6923⋊C5) |
| unambiguous semidirect product | (C19⋊#6923)⋊C5 |
| Fitting, socle, derived, Hall | C19×C61 ⋊ C4×C5 |
| Hall | C19×C61⋊C5 ⋊ C4 |
| Hall | C19⋊#6923 ⋊ C5 |
| Hall | C61⋊C5 ⋊ Dic19 |
| Sylow | C61 ⋊ C5×Dic19 |
| Sylow | C19 ⋊ #6923⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C61 | C4×C5 |
| prime radical | C19×D61⋊C5 | C2 |
| cosocle | C19×D61 | C2×C5 |
| LCS | G ▷ C19×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1159 |
Polycyclic presentation:
2,5,2,19,61|a^2=c,d^a=d^18,e^a=e^50,e^b=e^9,e^c=e^60167 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23180, 15);