Finite Group DatabasebetaFinite Group Databasebeta| order | 36972 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| Fitting, derived, Hall | C9×C79 ⋊ C22×C13 |
| Hall | C9×C79⋊C13 ⋊ C22 |
| Hall | D9×D79 ⋊ C13 |
| Hall | C79⋊C13 ⋊ C2×D9 |
| Sylow | C79 ⋊ C2×C13×D9 |
| Sylow | C9 ⋊ C2×D79⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C79 | C22×C13 |
| Frattini | C3 | D3×D79⋊C13 |
| socle | C3×C79 | C2×D3×C13 |
| LCS | G ▷ C9×C79 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 711 |
174 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36972, 33);