Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C7×Q8×C4⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ #34242 |
2286 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=h,b^2=h,c^2=f,d^2=fg,e^2=g,b^a=bf,c^a=cg,e^a=ef,i^a=i^6,d^b=df,i^c=i^6,i^d=i^6,i^e=i^6238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 330418);