Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#5425 |
148 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3,4,5,6,7)(9,11)(12,20,25,13,15,27,17,18,23,14,24,26)(16,21,22,19);(8,9)(10,11)(12,13,17,14)(15,19,24,21)(16,18,22,20)(23,27,25,26)161 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6433);