Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#5420 |
162 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 42 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) = 224 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3,4,5,6,7)(12,14,21)(13,24,26,17,18,27)(16,22,23)(19,25);(8,9,10,11)(12,13)(14,19)(15,18)(16,17)(20,24)(21,27)(22,25)(23,26)182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6429);