Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#5426 |
| derived | SL(2,𝔽3) ⋊ C2×C4×C7 |
158 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 158 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) = 448 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3,4,5,6,7)(12,18,23,17,14,26,16,24,21,13,22,27)(15,19,20,25);(8,9,10,11)(13,17)(14,15)(18,25)(19,24)(20,22)(21,23)182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6435);