Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D7×#1368 |
| Fitting | C7×#1368 ⋊ C2 |
| Sylow | C7 ⋊ C2×#1368 |
254 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#12067, AGL(1,𝔽7)×#1368 |
| maximal normal subgroup of | D7×#12067, AGL(1,𝔽7)×#1368 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 81118);