Finite Group DatabasebetaFinite Group Databasebeta| order | 784 |
| isoclinism | isoclinic class of D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C49⋊C8 |
| unambiguous semidirect product | (C2×C49)⋊C8 |
| derived, Sylow | C49 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D49 |
| commutator, hypocenter | C49 | C2×C8 |
| Frattini | C4×C7 | C2×D7 |
| Fitting | C2×C4×C49 | C2 |
| socle, prime radical | C22×C7 | Dic7 |
| cosocle | C4×C49 | C22 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C2×C4 | |
33 conjugacy classes of subgroups.
| transitive degree | μt(G) = 784 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C4×C49⋊C8, #13095843, C4⋊(C49⋊C8), … |
| maximal normal subgroup of | C4×C49⋊C8, #13095843, C4⋊(C49⋊C8), … |
| maximal quotient of | C4×C49⋊C8, C4⋊(C49⋊C8), C2×C49⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(784, 8);