Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C4×C7×#121 ⋊ C2 |
| Sylow | C7 ⋊ #36678 |
1686 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=f,b^2=f,e^2=g,b^a=bf,c^a=cg,d^a=dh,i^a=i^6,c^b=ch,d^c=dfh220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 376048);