Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×#2641 ⋊ C2 |
| Sylow | C7 ⋊ #25690 |
1072 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=e,c^2=f,d^2=e,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^6,c^b=cg,g^b=gh,i^b=i^6,d^c=dh,g^c=gh,i^c=i^6136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 224040);