Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C7×#2884 ⋊ C2 |
| Sylow | C7 ⋊ #60070 |
4892 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|a^2=g,e^2=h,b^a=bf,f^a=fh,g^b=gh,d^c=dh,i^c=i^6,i^d=i^6,i^e=i^6205 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1033045);