Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C7×#3025 ⋊ C2 |
| Sylow | C7 ⋊ #23882 |
1866 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^8,7|e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,g^a=gh,c^b=cg,e^b=eh,i^b=i^6,e^c=eh,f^c=fh,i^c=i^6,e^d=eh,f^d=fh,i^d=i^6136 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#23882 |
| maximal normal subgroup of | D7×#23882 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 200979);