Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#89423 |
| Sylow | C7 ⋊ C2×#383 |
624 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #13243418, #13243806, #13243834, … |
| maximal normal subgroup of | #13243418, #13243806, #13243834, … |
| maximal quotient of | C2×#11727156, C2×#11727155, C2×#11727157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5535);