Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C256 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊C256 |
| derived, Sylow | C7 ⋊ C256 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C128 | D7 |
| commutator, hypocenter | C7 | C256 |
| Fitting, cosocle | C7×C128 | C2 |
| socle, prime radical | C2×C7 | C128 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C128 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 263 |
| transitive degree | μt(G) = 1792 |
Polycyclic presentation:
2^8,7|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,g^2=h,i^a=i^6640 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 56093);