Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C22 |
| direct product | C3×(C2×D7)⋊C16 |
| Fitting | C2×C3×C7×C16 ⋊ C2 |
| Hall | C3×C7 ⋊ C22⋊C16 |
| Sylow | C7 ⋊ C3×C22⋊C16 |
132 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 66 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) = 672 |
A minimal faithful permutation representation — 2 generators on 30 points:
(1,2,3)(4,5,7,9,10,8,6)(12,14)(15,16,17,20,18,21,23,26,19,22,24,27,25,28,29,30);(5,6)(7,8)(9,10)(11,12)(13,14)408 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 455);