Finite Group DatabasebetaFinite Group Databasebeta| order | 36243 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C4027⋊C3 |
| unambiguous semidirect product | C4027⋊C32 |
| unambiguous semidirect product | (C3×C4027)⋊C3 |
| Fitting, socle | C3×C4027 ⋊ C3 |
| derived, Sylow | C4027 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C4027⋊C3 |
| commutator, cosocle, hypocenter | C4027 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C4027 | C3 |
| LCS | G ▷ C4027 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12081 |
4035 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36243, 3);