Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#5798 |
| Hall | C3×C7 ⋊ #518 |
| Sylow | C3 ⋊ C7×#518 |
676 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 382 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 — 4 generators on 22 points:
(1,2,3,4,5,6,7)(8,9,10)(16,20)(19,22);(17,21)(19,22);(15,17)(16,19)(18,21)(20,22);(9,10)(11,12,13,14)(15,16)(17,19)(18,20)(21,22)378 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10802);