Finite Group DatabasebetaFinite Group Databasebeta| order | 36756 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#16861391 |
| Fitting, derived, Hall | C9×C1021 ⋊ C4 |
| Sylow | C1021 ⋊ Dic9 |
| Sylow | C9 ⋊ #16861391 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C1021 | C4 |
| Frattini | C3 | C3⋊#16861391 |
| socle | C3×C1021 | Dic3 |
| prime radical | C3×D1021 | D3 |
| cosocle | C9×D1021 | C2 |
| LCS | G ▷ C9×C1021 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9189 |
Polycyclic presentation:
2^2,3,1021,3|a^2=b,c^3=e^2,c^a=c^2e,d^a=d^647,e^a=e^2,d^b=d^10202307 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36756, 11);