Finite Group DatabasebetaFinite Group Databasebeta| order | 23180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic1159 |
| unambiguous semidirect product | C19⋊(C5×Dic61) |
| derived, Hall | C19×C61 ⋊ C4×C5 |
| Hall | C5×C19×C61 ⋊ C4 |
| Hall | C5×C61 ⋊ Dic19 |
| Hall | C5×C19 ⋊ Dic61 |
| Sylow | C61 ⋊ C5×Dic19 |
| Sylow | C19 ⋊ C5×Dic61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D1159 |
| commutator, hypocenter | C19×C61 | C4×C5 |
| Frattini | C2 | C5×D1159 |
| Fitting, socle, prime radical | C2×C5×C19×C61 | C2 |
| cosocle | C2×C19×C61 | C2×C5 |
| LCS | G ▷ C19×C61 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23180 |
5810 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23180, 5);