Finite Group DatabasebetaFinite Group Databasebeta| order | 18772 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic361 |
| unambiguous semidirect product | C361⋊(C4×C13) |
| derived, Sylow | C361 ⋊ C4×C13 |
| Hall | C13×C361 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D361 |
| commutator, hypocenter | C361 | C4×C13 |
| Frattini | C2×C19 | C13×D19 |
| Fitting | C2×C13×C361 | C2 |
| socle, prime radical | C2×C13×C19 | D19 |
| cosocle | C2×C361 | C2×C13 |
| LCS | G ▷ C361 | |
| UCS | C1 ◁ C2×C13 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18772 |
4732 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18772, 3);