Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4⋊C4×C22⋊D7 |
| Fitting | C22×C7×C4⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ D4×C4⋊C4 |
776 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | #102×C22⋊D7, #13369200, #103×C22⋊D7, … |
| maximal normal subgroup of | #102×C22⋊D7, #13369200, #103×C22⋊D7, … |
| maximal quotient of | C4⋊C4×(C2×D7)⋊C4, C4⋊C4×C22⋊Dic7, C4⋊C4×Dic7⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14398);