Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C42 |
No aliases for this group.
| Fitting | C2×C7×#390 ⋊ C2 |
| Sylow | C7 ⋊ #14358 |
3538 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=h,b^2=e,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,i^c=i^6232 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 96859);