Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22⋊C4×C22⋊D7 |
| Fitting | C22×C7×C22⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ D4×C22⋊C4 |
1252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | #13369116, #99×C22⋊D7, #13369924, … |
| maximal normal subgroup of | #13369116, #99×C22⋊D7, #13369924, … |
| maximal quotient of | C22⋊C4×(C2×D7)⋊C4, C22⋊C4×C22⋊Dic7, C22⋊C4×Dic7⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14333);