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×#383 ⋊ C2 |
| Sylow | C7 ⋊ #14661 |
2502 conjugacy classes of subgroups; only the 371 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 371 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=f,b^2=h,d^2=e,b^a=be,c^a=cf,c^b=cg,d^b=def,d^c=de,i^c=i^6220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 100606);