Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| isoclinism | isoclinic class of #2865⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #14690⋊C7 |
| Fitting, Sylow | #14690 ⋊ C7 |
| derived | C43 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #2865⋊C7 |
| commutator, hypocenter | C43 | C4×C7 |
| Frattini, socle | C24 | C2×AGL(1,𝔽8) |
| Fitting | #14690 | C7 |
| prime radical | C2×C43⋊C7 | C2 |
| cosocle | C2×C43 | C2×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 56 |
Polycyclic presentation:
7,2^8|b^2=i,c^2=gh,d^2=fg,e^2=f,b^a=bfg,c^a=di,d^a=ceh,e^a=deh,f^a=g,g^a=fh,h^a=gh,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, 1083477);