Finite Group DatabasebetaFinite Group Databasebeta| order | 36162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D6027 |
| unambiguous semidirect product | C41⋊(C3⋊D147) |
| unambiguous semidirect product | C49⋊(C3⋊D123) |
| Fitting, derived, Hall | C32×C41×C49 ⋊ C2 |
| Hall | C41×C49 ⋊ C3⋊D3 |
| Hall | C32×C49 ⋊ D41 |
| Hall | C32×C41 ⋊ D49 |
| Sylow | C49 ⋊ C3⋊D123 |
| Sylow | C41 ⋊ C3⋊D147 |
| Sylow | C32 ⋊ D2009 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C41×C49 | C2 |
| Frattini | C7 | C3⋊D861 |
| socle | C32×C7×C41 | D7 |
| LCS | G ▷ C32×C41×C49 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18081 |
Polycyclic presentation:
2,3^2,7,41,7|d^7=f^6,b^a=b^2,c^a=c^2,d^a=d^6f,e^a=e^40,f^a=f^69042 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36162, 32);