Finite Group DatabasebetaFinite Group Databasebeta| order | 784 |
| isoclinism | isoclinic class of D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×Dic49 |
| unambiguous semidirect product | C49⋊C42 |
| derived, Sylow | C49 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D49 |
| commutator, hypocenter | C49 | C42 |
| Frattini, socle, prime radical | C22×C7 | C2×D7 |
| Fitting | C2×C4×C49 | C2 |
| cosocle | C22×C49 | C22 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C2×C4 | |
45 conjugacy classes of subgroups.
| transitive degree | μt(G) = 784 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C8×Dic49, Dic49⋊C8, #13095856, … |
| maximal normal subgroup of | C8×Dic49, Dic49⋊C8, #13095856, … |
| maximal quotient of | C4×C49⋊C8, #13095843, C8×Dic49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(784, 10);