Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×D7×SD16 |
| Fitting | C22×C7×SD16 ⋊ C2 |
| Sylow | C7 ⋊ C23×SD16 |
1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1877, D7×#1880, #13355223, … |
| maximal normal subgroup of | D7×#1877, D7×#1880, #13355223, … |
| maximal quotient of | C22×D7×#102, C22×D7×#103, C22×D7×#106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19007);