Finite Group DatabasebetaFinite Group Databasebeta| order | 36778 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C37⋊(D71⋊C7) |
| unambiguous semidirect product | (C71⋊C7)⋊D37 |
| unambiguous semidirect product | D2627⋊C7 |
| Fitting, socle, derived, Hall | C37×C71 ⋊ C2×C7 |
| Hall | C37×C71⋊C7 ⋊ C2 |
| Hall | D2627 ⋊ C7 |
| Hall | C71⋊C7 ⋊ D37 |
| Sylow | C71 ⋊ C7×D37 |
| Sylow | C37 ⋊ D71⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C71 | C2×C7 |
| LCS | G ▷ C37×C71 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2627 |
Polycyclic presentation:
2,7,37,71|c^a=c^36,d^a=d^70,d^b=d^45325 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36778, 12);