Finite Group DatabasebetaFinite Group Databasebeta| order | 36162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C41⋊#11725075 |
| derived, Hall | C72×C41 ⋊ C2×C9 |
| Hall | C41×#89205 ⋊ C2 |
| Hall | C7×D287 ⋊ C9 |
| Hall | #89205 ⋊ D41 |
| Sylow | C72 ⋊ C9×D41 |
| Sylow | C41 ⋊ #11725075 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C41⋊#64422 |
| commutator, hypocenter | C72×C41 | C2×C9 |
| Fitting, socle, cosocle | C3×C72×C41 | C2×C3 |
| prime radical | C3×C7×D287 | C3 |
| LCS | G ▷ C72×C41 | |
| UCS | C1 ◁ C3 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5166 |
Polycyclic presentation:
2,3,7^2,41,3|b^3=f,c^a=c^6,e^a=e^40,c^b=c^2,d^b=d^41191 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36162, 44);