Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of #6400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#89287 |
| Sylow | C7 ⋊ C2×#358 |
232 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 101 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 | #13269004, C4×#89287, #13269014, … |
| maximal normal subgroup of | #13269004, C4×#89287, #13269014, … |
| maximal quotient of | C2×#11725278, #13263774, #13263826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3121);