Finite Group DatabasebetaFinite Group Databasebeta| order | 36036 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | Dic11×#11717941 |
| unambiguous semidirect product | C11⋊(C4×#11717941) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D11×#63270 |
| commutator, hypocenter | C7×C11×C13 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C7×C11×C13 | C2×C3 |
| LCS | G ▷ C7×C11×C13 | |
| UCS | C1 ◁ C2×C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36036 |
1386 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36036, 27);