Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #6400 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#89285 |
| Hall | C3×C7 ⋊ #367 |
| Sylow | C7 ⋊ C3×#367 |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 1344 |
A minimal faithful permutation representation — 2 generators on 30 points:
(1,2,3)(4,5,7,9,10,8,6)(11,12,13,14)(16,20)(17,24)(18,25)(21,28)(22,29)(23,27)(26,30);(5,6)(7,8)(9,10)(15,16,17,21,25,28,30,20,19,23,26,29,18,22,24,27)192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 439);