Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C4×C7×#117 ⋊ C2 |
| Sylow | C7 ⋊ #34803 |
1812 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=gh,b^2=g,d^2=g,e^2=f,b^a=bf,c^a=cg,c^b=ch,d^b=dh,i^b=i^6316 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 339313);