Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Fitting | C4×C7×H(5,𝔽2) ⋊ C2 |
| Sylow | C7 ⋊ #62652 |
11674 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|a^2=h,b^a=bg,f^a=fg,e^b=eg,d^c=dg,i^f=i^6334 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1076184);