Finite Group DatabasebetaFinite Group Databasebeta| order | 36778 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×D259 |
| unambiguous semidirect product | C7⋊(C71×D37) |
| unambiguous semidirect product | C37⋊(D7×C71) |
| Fitting, socle, Hall | C7×C37×C71 ⋊ C2 |
| derived, Hall | C7×C37 ⋊ C2×C71 |
| Hall | C37×C71 ⋊ D7 |
| Hall | C7×C71 ⋊ D37 |
| Sylow | C37 ⋊ D7×C71 |
| Sylow | C7 ⋊ C71×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | D259 |
| commutator, cosocle, hypocenter | C7×C37 | C2×C71 |
| Frattini | C1 | G |
| Fitting, socle | C7×C37×C71 | C2 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C71 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18389 |
9301 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36778, 8);