Finite Group DatabasebetaFinite Group Databasebeta| order | 784 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C7 |
| direct product | C2×C4×C7⋊D7 |
| Fitting | C2×C4×C72 ⋊ C2 |
| derived, Sylow | C72 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | C7⋊D7 |
| commutator, hypocenter | C72 | C22×C4 |
| Frattini | C2 | C22×C7⋊D7 |
| Fitting | C2×C4×C72 | C2 |
| socle | C22×C72 | C22 |
| prime radical | C22×C7⋊D7 | C2 |
| cosocle | C2×C72 | C23 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C4 | |
270 conjugacy classes of subgroups.
| transitive degree | μt(G) = 392 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #13096049, #13096137, #13096215, … |
| maximal normal subgroup of | #13096049, #13096137, #13096215, … |
| maximal quotient of | C4×#87648, C42×C7⋊D7, #13096512, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(784, 147);