Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22 |
| direct product | C4⋊Q8×AGL(1,𝔽8) |
| unambiguous semidirect product | C4⋊(Q8×AGL(1,𝔽8)) |
| unambiguous semidirect product | (C4×AGL(1,𝔽8))⋊Q8 |
| unambiguous semidirect product | (C23×C4⋊Q8)⋊C7 |
| Fitting, Sylow | C23×C4⋊Q8 ⋊ C7 |
997 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 997 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1083526);