Finite Group DatabasebetaFinite Group Databasebeta| order | 36974 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D2641 |
| unambiguous semidirect product | C19⋊(C7×D139) |
| unambiguous semidirect product | C139⋊(C7×D19) |
| Fitting, socle, Hall | C7×C19×C139 ⋊ C2 |
| derived, Hall | C19×C139 ⋊ C2×C7 |
| Hall | C7×C139 ⋊ D19 |
| Sylow | C139 ⋊ C7×D19 |
| Hall | C7×C19 ⋊ D139 |
| Sylow | C19 ⋊ C7×D139 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D2641 |
| commutator, cosocle, hypocenter | C19×C139 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C139 | C2 |
| LCS | G ▷ C19×C139 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18487 |
9254 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36974, 4);