Finite Group DatabasebetaFinite Group Databasebeta| order | 33606 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D16803 |
| unambiguous semidirect product | C9⋊D1867 |
| unambiguous semidirect product | C1867⋊D9 |
| Fitting, derived, Hall | C9×C1867 ⋊ C2 |
| Sylow | C1867 ⋊ D9 |
| Sylow | C9 ⋊ D1867 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C1867 | C2 |
| Frattini | C3 | D5601 |
| socle | C3×C1867 | D3 |
| LCS | G ▷ C9×C1867 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1876 |
| transitive degree | μt(G) = 16803 |
A minimal faithful permutation representation — 2 generators on 1876 points:
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presentation:
2,3,1867,3|b^3=d^2,b^a=b^2d,c^a=c^1866,d^a=d^28403 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33606, 6);