Finite Group DatabasebetaFinite Group Databasebeta| order | 33246 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D16623 |
| unambiguous semidirect product | C9⋊D1847 |
| unambiguous semidirect product | C1847⋊D9 |
| Fitting, derived, Hall | C9×C1847 ⋊ C2 |
| Sylow | C1847 ⋊ D9 |
| Sylow | C9 ⋊ D1847 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C1847 | C2 |
| Frattini | C3 | D5541 |
| socle | C3×C1847 | D3 |
| LCS | G ▷ C9×C1847 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1856 |
| transitive degree | μt(G) = 16623 |
A minimal faithful permutation representation — 2 generators on 1856 points:
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presentation:
2,3,1847,3|b^3=d^2,b^a=b^2d,c^a=c^1846,d^a=d^28313 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33246, 4);