Finite Group DatabasebetaFinite Group Databasebeta| order | 784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q8×D49 |
| Fitting | Q8×C49 ⋊ C2 |
| Sylow | C49 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D49 |
| commutator, cosocle | C2×C49 | C23 |
| Frattini, socle | C2×C7 | C22×D7 |
| Fitting | Q8×C49 | C2 |
| prime radical | C2×D49 | C22 |
| hypercenter | Q8 | D49 |
| hypocenter | C49 | C2×Q8 |
| LCS | G ▷ C2×C49 ▷ C49 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
57 conjugacy classes of subgroups.
| transitive degree | μt(G) = 392 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×D49, #13095944, Q16×D49, … |
| maximal normal subgroup of | SD16×D49, #13095944, Q16×D49, … |
| maximal quotient of | #13095916, #13095917, #13095918, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(784, 33);