Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#4649 |
| Hall | C3×C7 ⋊ C4×C4⋊C4 |
| Sylow | C3 ⋊ C4×C7×C4⋊C4 |
388 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 1344 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2,3,4,5,6,7)(8,9,10)(11,12,13,14)(15,17,18,16)(20,22);(15,16,18,17)(19,20,21,22);(9,10)(15,16,18,17)420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4974);