Finite Group DatabasebetaFinite Group Databasebeta| order | 33782 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D127⋊C7 |
| unambiguous semidirect product | D127⋊(C7×C19) |
| unambiguous semidirect product | (C127⋊C7)⋊(C2×C19) |
| unambiguous semidirect product | (C19×D127)⋊C7 |
| Fitting, socle, Hall | C19×C127 ⋊ C2×C7 |
| derived, Sylow | C127 ⋊ C2×C7×C19 |
| Hall | C19×C127⋊C7 ⋊ C2 |
| Hall | C19×D127 ⋊ C7 |
| Hall | C127⋊C7 ⋊ C2×C19 |
| Hall | D127 ⋊ C7×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D127⋊C7 |
| commutator, cosocle, hypocenter | C127 | C2×C7×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C127 | C2×C7 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2413 |
437 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33782, 10);