Finite Group DatabasebetaFinite Group Databasebeta| order | 33708 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D2809 |
| unambiguous semidirect product | (D3×C2809)⋊C2 |
| unambiguous semidirect product | (C3×D2809)⋊C2 |
| unambiguous semidirect product | D8427⋊C2 |
| Fitting, derived, Hall | C3×C2809 ⋊ C22 |
| Sylow | C2809 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D2809 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C2809 | C22 |
| Frattini | C53 | D3×D53 |
| socle | C3×C53 | C2×D53 |
| LCS | G ▷ C3×C2809 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8427 |
4218 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33708, 8);