Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C4×D7×C4⋊C4 |
| Fitting | C4×C7×C4⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ C2×C4×C4⋊C4 |
928 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1279, #13243330, #13243366, … |
| maximal normal subgroup of | D7×#1279, #13243330, #13243366, … |
| maximal quotient of | C4×D7×#95, C4×#89421, C4×C4⋊C4×Dic7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5960);