Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×#1804 ⋊ C2 |
| Sylow | C7 ⋊ #22549 |
1118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=g,b^2=e,c^2=eh,d^2=eh,f^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^6,c^b=ch,d^b=de,i^b=i^6,f^c=fh172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 186458);