Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C23 |
| direct product | C3×#89321 |
| Hall | C3×C7 ⋊ #342 |
| Sylow | C7 ⋊ C3×#342 |
284 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 336 |
A minimal faithful permutation representation — 2 generators on 22 points:
(1,2,3)(4,5,7,9,10,8,6)(11,12,13,14)(15,17)(16,19)(18,22)(20,21);(5,6)(7,8)(9,10)(15,16)(17,21,22,19)(18,20)246 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 476);