Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#949 |
| Fitting | C3×#41×C19 ⋊ C2 |
| Hall | C3×C19 ⋊ AGL(1,ℤ/8) |
| Sylow | C3 ⋊ C19×AGL(1,ℤ/8) |
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 456 |
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)(23,24)(25,30)(26,28)(27,29);(24,28)(27,30);(21,22)(24,27)(25,29)(28,30)399 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 928);