Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Fitting | C7×#3428 ⋊ C2 |
| Sylow | C7 ⋊ C4×#585 |
11346 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=h,e^2=h,f^2=g,b^a=bg,d^a=dg,c^b=cg,i^e=i^6340 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1076180);