Finite Group DatabasebetaFinite Group Databasebeta| order | 1456 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×Dic7⋊C4 |
| unambiguous semidirect product | Dic7⋊(C4×C13) |
| Hall | C7×C13 ⋊ C4⋊C4 |
| Sylow | C7 ⋊ C13×C4⋊C4 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 1456 |
A minimal faithful permutation representation — 2 generators on 28 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,19,20,18,16)(21,22,23,24)(26,28);(15,16)(17,18)(19,20)(25,26,27,28)442 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1456, 56);