Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C7×H(3,ℤ/4) ⋊ C2 |
| Sylow | C7 ⋊ #23414 |
1980 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|e^2=h,b^a=be,c^a=cf,e^a=eh,g^a=gh,i^a=i^6,c^b=cg,e^b=eh,f^b=fh,i^b=i^6,d^c=dh,i^c=i^6178 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 196593);