Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C4×(C22⋊D7)⋊C4 |
| Fitting | C4×C7×C22⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ C42×D4 |
924 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C8×(C22⋊D7)⋊C4, #13352139, #13352144, … |
| maximal normal subgroup of | C8×(C22⋊D7)⋊C4, #13352139, #13352144, … |
| maximal quotient of | C4×#89438, C4×C22⋊C4×Dic7, C4×#89421, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5645);