Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C26×C42 |
| direct product | Dic7×H(3,𝔽4) |
| Sylow | C7 ⋊ C4×H(3,𝔽4) |
2664 conjugacy classes of subgroups; only the 1093 normal subgroups are shown.
This group has 2664 conjugacy classes of subgroups — too many to draw. Only its 1093 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 332274);