Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| isoclinism | isoclinic class of #2846⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #14679⋊C7 |
| unambiguous semidirect product | #90631⋊C4 |
| Fitting, Sylow | #14679 ⋊ C7 |
| derived | C26 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #2846⋊C7 |
| commutator, hypocenter | C26 | C4×C7 |
| Frattini, socle | C24 | C2×AGL(1,𝔽8) |
| Fitting | #14679 | C7 |
| prime radical | C2×#90631 | C2 |
| cosocle | C27 | C2×C7 |
| LCS | G ▷ C26 | |
| UCS | C1 ◁ C2 | |
2236 conjugacy classes of subgroups; only the 11 normal subgroups are shown.
This group has 2236 conjugacy classes of subgroups — too many to draw. Only its 11 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 28 |
Polycyclic presentation:
7,2^8|b^2=i,b^a=bcdefi,c^a=cdefg,d^a=ch,e^a=cegi,f^a=fgh,g^a=f,h^a=fh,i^a=fghi,c^b=cf,d^b=dg,e^b=eh40 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1083476);