Finite Group DatabasebetaFinite Group Databasebeta| order | 36722 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×D427 |
| unambiguous semidirect product | C7⋊(C43×D61) |
| unambiguous semidirect product | C61⋊(D7×C43) |
| Fitting, socle, Hall | C7×C43×C61 ⋊ C2 |
| derived, Hall | C7×C61 ⋊ C2×C43 |
| Hall | C43×C61 ⋊ D7 |
| Hall | C7×C43 ⋊ D61 |
| Sylow | C61 ⋊ D7×C43 |
| Sylow | C7 ⋊ C43×D61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D427 |
| commutator, cosocle, hypocenter | C7×C61 | C2×C43 |
| Frattini | C1 | G |
| Fitting, socle | C7×C43×C61 | C2 |
| LCS | G ▷ C7×C61 | |
| UCS | C1 ◁ C43 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18361 |
9245 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36722, 7);