Finite Group DatabasebetaFinite Group Databasebeta| order | 18772 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C13×D361 |
| unambiguous semidirect product | C361⋊(C22×C13) |
| unambiguous semidirect product | (C2×C361)⋊(C2×C13) |
| Fitting | C2×C13×C361 ⋊ C2 |
| derived, Sylow | C361 ⋊ C22×C13 |
| Hall | C13×C361 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D361 |
| commutator, cosocle, hypocenter | C361 | C22×C13 |
| Frattini | C19 | C2×C13×D19 |
| Fitting | C2×C13×C361 | C2 |
| socle | C2×C13×C19 | D19 |
| LCS | G ▷ C361 | |
| UCS | C1 ◁ C2×C13 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9386 |
4732 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18772, 9);