Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10597283⋊C3 |
| Fitting | D8×C19 ⋊ C2×C3 |
| Hall | #10597283 ⋊ C3 |
| Hall | C19⋊C3 ⋊ D16 |
| Sylow | C19 ⋊ C3×D16 |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^2,3,2^3,19|d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^18,d^b=de,e^b=ef,g^c=g^1154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 36);