Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | Dic7×#124 |
| Sylow | C7 ⋊ C4×#124 |
652 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 249 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | Dic7×#329, #13244720, #13244728, … |
| maximal normal subgroup of | Dic7×#329, #13244720, #13244728, … |
| maximal quotient of | Dic7×#388, Dic7×#390, Dic7×#391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15163);