Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C22×D4×Dic7 |
| Sylow | C7 ⋊ C22×C4×D4 |
2528 conjugacy classes of subgroups; only the 1197 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 1197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #13259216, #13259220, #13259360, … |
| maximal normal subgroup of | #13259216, #13259220, #13259360, … |
| maximal quotient of | C22×C22⋊C4×Dic7, C22×C4⋊C4×Dic7, C2×C4×D4×Dic7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19061);