Finite Group DatabasebetaFinite Group Databasebeta| order | 784 |
| isoclinism | isoclinic class of #87640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#87640 |
| Sylow | C72 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D72 |
| commutator, cosocle | C2×C72 | C23 |
| Frattini | C2 | C2×D72 |
| Fitting, socle | C22×C72 | C22 |
| hypocenter | C72 | C2×D4 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C22 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
94 conjugacy classes — view the full character table.
| maximal subgroup of | #13096192, #13096309, C4×#87640, … |
| maximal normal subgroup of | #13096192, #13096309, C4×#87640, … |
| maximal quotient of | #13096265, #13096267, #13096277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(784, 131);