Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#940 |
| Fitting | C2×C3×D4×C19 ⋊ C2 |
| Hall | C3×C19 ⋊ #127 |
| Sylow | C3 ⋊ C19×#127 |
216 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 912 |
A minimal faithful permutation representation — 3 generators on 30 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22)(24,26)(28,30);(27,28,29,30);(21,22)(23,24)(25,26)(28,30)456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 912);