Finite Group DatabasebetaFinite Group Databasebeta| order | 33782 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊(D127⋊C7) |
| unambiguous semidirect product | (C127⋊C7)⋊D19 |
| unambiguous semidirect product | D2413⋊C7 |
| Fitting, socle, derived, Hall | C19×C127 ⋊ C2×C7 |
| Hall | C19×C127⋊C7 ⋊ C2 |
| Hall | D2413 ⋊ C7 |
| Hall | C127⋊C7 ⋊ D19 |
| Sylow | C127 ⋊ C7×D19 |
| Sylow | C19 ⋊ D127⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C127 | C2×C7 |
| LCS | G ▷ C19×C127 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2413 |
Polycyclic presentation:
2,7,19,127|c^a=c^18,d^a=d^126,d^b=d^4248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33782, 12);