Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #1132 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×#89252 |
| Hall | C3×C7 ⋊ #334 |
| Sylow | C7 ⋊ C3×#334 |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 1344 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3)(4,5,7,9,10,8,6)(19,20,21,23,22,24,25,26);(5,6)(7,8)(9,10)(11,12,13,15,14,16,17,18)(20,23)(21,25)(24,26)372 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 405);