Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C2×C4×C7×C22⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ #34057 |
2946 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=h,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, 328241);