Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C7×#2923 ⋊ C2 |
| Sylow | C7 ⋊ #60123 |
2122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=g,c^2=f,g^2=h,b^a=bf,e^a=eh,d^b=dh,i^c=i^6,i^e=i^6220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1033337);