Finite Group DatabasebetaFinite Group Databasebeta| order | 37772 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊(Dic71⋊C7) |
| unambiguous semidirect product | (C71⋊C7)⋊Dic19 |
| unambiguous semidirect product | Dic1349⋊C7 |
| derived, Hall | C19×C71 ⋊ C4×C7 |
| Hall | C19×C71⋊C7 ⋊ C4 |
| Hall | Dic1349 ⋊ C7 |
| Hall | C71⋊C7 ⋊ Dic19 |
| Sylow | C71 ⋊ C7×Dic19 |
| Sylow | C19 ⋊ Dic71⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C19⋊(D71⋊C7) |
| commutator, hypocenter | C19×C71 | C4×C7 |
| Fitting, socle, cosocle | C2×C19×C71 | C2×C7 |
| prime radical | C2×C19×C71⋊C7 | C2 |
| LCS | G ▷ C19×C71 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5396 |
Polycyclic presentation:
2,7,19,71,2|a^2=e,c^a=c^18,d^a=d^70,d^b=d^45344 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37772, 12);