Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#89953 |
| Sylow | C7 ⋊ C2×#494 |
552 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #13272012, #13272030, #13272050, … |
| maximal normal subgroup of | #13272012, #13272030, #13272050, … |
| maximal quotient of | C2×#11729050, C2×#11728966, C2×#11729114, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16089);