Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#90443 |
| Fitting | C2×C7×#131 ⋊ C2 |
| Sylow | C7 ⋊ C2×#576 |
1512 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
164 conjugacy classes — view the full character table.
| maximal subgroup of | #13269481, #13269484, #13269491, … |
| maximal normal subgroup of | #13269481, #13269484, #13269491, … |
| maximal quotient of | C2×#11741242, C2×#11741230, C2×#11736005, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18995);