Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C23×C7×C22⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ #14718 |
4034 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|c^2=e,b^a=be,c^a=cf,d^a=dh,i^a=i^6,c^b=cg304 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 100969);