Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #89246 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#89246 |
| Fitting | C3×C7×#95 ⋊ C2 |
| Hall | C3×C7 ⋊ #327 |
| Sylow | C7 ⋊ C3×#327 |
180 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 180 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) = 26 |
| transitive degree | μt(G) = 336 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3)(4,5,7,9,10,8,6)(11,13)(12,15,16,17)(14,18)(20,23,24,25);(5,6)(7,8)(9,10)(11,12)(13,17)(14,16)(15,18)(19,20)(21,23)(22,24)(25,26)237 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 400);