Finite Group DatabasebetaFinite Group Databasebeta| order | 23180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊(Dic61⋊C5) |
| unambiguous semidirect product | Dic1159⋊C5 |
| derived, Hall | C19×C61 ⋊ C4×C5 |
| Hall | C19×C61⋊C5 ⋊ C4 |
| Hall | Dic1159 ⋊ C5 |
| Hall | C61⋊C5 ⋊ Dic19 |
| Sylow | C61 ⋊ C5×Dic19 |
| Sylow | C19 ⋊ Dic61⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C19⋊(D61⋊C5) |
| commutator, hypocenter | C19×C61 | C4×C5 |
| Fitting, socle, cosocle | C2×C19×C61 | C2×C5 |
| prime radical | C2×C19×C61⋊C5 | C2 |
| LCS | G ▷ C19×C61 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4636 |
Polycyclic presentation:
2,5,19,61,2|a^2=e,c^a=c^18,d^a=d^60,d^b=d^9338 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23180, 12);