Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | Dic7×#106 |
| Sylow | C7 ⋊ C4×#106 |
280 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #13269043, Dic7×#360, #13269179, … |
| maximal normal subgroup of | #13269043, Dic7×#360, #13269179, … |
| maximal quotient of | Dic7×#334, #13244987, #13245005, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3072);