Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q16×D28 |
| Fitting | C4×C7×Q16 ⋊ C2 |
| Sylow | C7 ⋊ D4×Q16 |
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
119 conjugacy classes — view the full character table.
| maximal subgroup of | #13267233, #13267237, #13267261, … |
| maximal normal subgroup of | #13267233, #13267237, #13267261, … |
| maximal quotient of | #13343988, #13344003, #13344018, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 11944);