Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C4×C7×#117 ⋊ C2 |
| Sylow | C7 ⋊ #34060 |
2458 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=h,d^2=f,e^2=g,b^a=bf,c^a=cg,d^a=df,c^b=cf,i^c=i^6328 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 328267);