Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of #6400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#89288 |
| Sylow | C7 ⋊ C2×#368 |
144 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #13269184, #13269186, #13269189, … |
| maximal normal subgroup of | #13269184, #13269186, #13269189, … |
| maximal quotient of | C2×#11725275, C2×#11725276, #13265379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3202);