Finite Group DatabasebetaFinite Group Databasebeta| order | 784 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×C22⋊Dic7 |
| unambiguous semidirect product | C22⋊(C7×Dic7) |
| Sylow | C72 ⋊ C22⋊C4 |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 56 |
238 conjugacy classes — view the full character table.
| maximal subgroup of | #13096072, #13096073, C7×#6380, … |
| maximal normal subgroup of | #13096072, #13096073, C7×#6380, … |
| maximal quotient of | C7×C22⋊(C7⋊C8), C7×C7⋊#95, C7×#6408, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(784, 79);