Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C42 |
No aliases for this group.
| Fitting | C2×C4×C7×C4⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ #13785 |
2470 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=g,b^2=h,c^2=fg,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,i^c=i^6328 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 90872);