Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | D7×#343 |
| Fitting | C7×#343 ⋊ C2 |
| Sylow | C7 ⋊ C2×#343 |
432 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 145 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×#1345, D7×#1346, #13264000, … |
| maximal normal subgroup of | D7×#1345, D7×#1346, #13264000, … |
| maximal quotient of | D7×#1280, #13243391, #13243394, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1508);