Finite Group DatabasebetaFinite Group Databasebeta| order | 36722 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×D301 |
| unambiguous semidirect product | C7⋊(C61×D43) |
| unambiguous semidirect product | C43⋊(D7×C61) |
| Fitting, socle, Hall | C7×C43×C61 ⋊ C2 |
| derived, Hall | C7×C43 ⋊ C2×C61 |
| Hall | C43×C61 ⋊ D7 |
| Hall | C7×C61 ⋊ D43 |
| Sylow | C43 ⋊ D7×C61 |
| Sylow | C7 ⋊ C61×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | D301 |
| commutator, cosocle, hypocenter | C7×C43 | C2×C61 |
| Frattini | C1 | G |
| Fitting, socle | C7×C43×C61 | C2 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C61 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18361 |
9272 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36722, 8);