Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#4491 |
| Fitting | C3×C7×#107 ⋊ C2 |
| Hall | C3×C7 ⋊ #357 |
| Sylow | C3 ⋊ C7×#357 |
132 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 672 |
A minimal faithful permutation representation — 2 generators on 30 points:
(1,2,3,4,5,6,7)(8,9,10)(11,12,13,14)(16,20)(17,24)(18,25)(21,22)(23,29)(26,30)(27,28);(9,10)(15,16)(17,20)(18,27)(19,23)(21,24)(22,25)(26,29)(28,30)252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 562);