Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C8 · Schur multiplier (H2) = C4 |
| direct product | C7×#4454 |
| Hall | C3×C7 ⋊ #322 |
| Sylow | C3 ⋊ C7×#322 |
132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 1344 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3,4,5,6,7)(8,9,10)(11,12,13,15,14,16,17,18)(20,23)(24,26);(9,10)(19,20,21,24,22,23,25,26)504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 525);