Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C2 |
| direct product | C3×Dic7⋊C16 |
| Hall | C3×C7 ⋊ C4⋊C16 |
| Sylow | C7 ⋊ C3×C4⋊C16 |
100 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)(12,14)(15,16,17,20,18,21,23,26,19,22,24,27,25,28,29,30);(5,6)(7,8)(9,10)(11,12,13,14)408 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 450);