Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D7×#101 |
| Fitting | C2×C7×#101 ⋊ C2 |
| Sylow | C7 ⋊ C22×#101 |
736 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1394, #13268779, #13271332, … |
| maximal normal subgroup of | D7×#1394, #13268779, #13271332, … |
| maximal quotient of | C2×D7×#324, D7×#1461, C2×#11725879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 10915);