Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | D7×#353 |
| Fitting | C7×#353 ⋊ C2 |
| Sylow | C7 ⋊ C2×#353 |
368 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 56 |
65 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1402, #13274017, D7×#1408, … |
| maximal normal subgroup of | D7×#1402, #13274017, D7×#1408, … |
| maximal quotient of | D7×#1318, D7×#1325, #13263063, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1669);