Finite Group DatabasebetaFinite Group Databasebeta| order | 36756 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊(C1021⋊C9) |
| unambiguous semidirect product | C1021⋊(C22⋊C9) |
| derived, Hall | C22×C1021 ⋊ C9 |
| Sylow | C1021 ⋊ C22⋊C9 |
| Sylow | C22 ⋊ C1021⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊(C1021⋊C3) |
| commutator, hypocenter | C22×C1021 | C9 |
| Fitting, socle, prime radical, cosocle | C22×C3×C1021 | C3 |
| LCS | G ▷ C22×C1021 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18378 |
Polycyclic presentation:
3,2^2,1021,3|a^3=e,b^a=c,c^a=bc,d^a=d^6524092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36756, 13);