Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#6471 |
| Fitting | C4×C7×M16 ⋊ C2 |
| Sylow | C7 ⋊ C4×AGL(1,ℤ/8) |
548 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
164 conjugacy classes — view the full character table.
| maximal subgroup of | #13248419, #13248421, #13248433, … |
| maximal normal subgroup of | #13248419, #13248421, #13248433, … |
| maximal quotient of | C8×#6471, #13323383, #13323405, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 10736);