Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#89857 |
| Fitting | C2×C7×C4⋊Q8 ⋊ C2 |
| Sylow | C7 ⋊ C2×#492 |
656 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 197 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 | #13249083, #13249085, #13249087, … |
| maximal normal subgroup of | #13249083, #13249085, #13249087, … |
| maximal quotient of | C2×#11729086, C2×#11729113, C2×#11729114, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15411);