Finite Group DatabasebetaFinite Group Databasebeta| order | 23180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#6923⋊C5 |
| unambiguous semidirect product | #6923⋊(C5×C19) |
| unambiguous semidirect product | (C19×#6923)⋊C5 |
| Fitting, socle, Hall | C19×C61 ⋊ C4×C5 |
| derived, Sylow | C61 ⋊ C4×C5×C19 |
| Hall | C19×C61⋊C5 ⋊ C4 |
| Hall | C19×#6923 ⋊ C5 |
| Hall | C61⋊C5 ⋊ C4×C19 |
| Hall | #6923 ⋊ C5×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #6923⋊C5 |
| commutator, hypocenter | C61 | C4×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C61 | C4×C5 |
| prime radical | C19×D61⋊C5 | C2 |
| cosocle | D61 | C2×C5×C19 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1159 |
437 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23180, 14);