Finite Group DatabasebetaFinite Group Databasebeta| order | 33564 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D2797 |
| unambiguous semidirect product | (D3×C2797)⋊C2 |
| unambiguous semidirect product | (C3×D2797)⋊C2 |
| unambiguous semidirect product | D8391⋊C2 |
| Fitting, socle, derived, Hall | C3×C2797 ⋊ C22 |
| Sylow | C2797 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D2797 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C2797 | C22 |
| LCS | G ▷ C3×C2797 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8391 |
4200 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33564, 12);