Finite Group DatabasebetaFinite Group Databasebeta| order | 33282 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D5547 |
| unambiguous semidirect product | C1849⋊(C3⋊D3) |
| Fitting, derived, Hall | C32×C1849 ⋊ C2 |
| Sylow | C1849 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ D1849 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C1849 | C2 |
| Frattini | C43 | C3⋊D129 |
| socle | C32×C43 | D43 |
| LCS | G ▷ C32×C1849 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16641 |
Polycyclic presentation:
2,3^2,43^2|d^43=e^42,b^a=b^2,c^a=c^2,d^a=d^42e,e^a=e^428322 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33282, 16);