Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#10597286 |
| Hall | C3×C19 ⋊ Q32 |
| Sylow | C19 ⋊ C3×Q32 |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 54 |
| transitive degree | μt(G) = 1824 |
222 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 168);