Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D4×(C2×D7)⋊C4 |
| Fitting | C2×C4×C7×D4 ⋊ 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 | #13369501, #13369502, #13369509, … |
| maximal normal subgroup of | #13369501, #13369502, #13369509, … |
| maximal quotient of | C22⋊C4×(C2×D7)⋊C4, C4⋊C4×(C2×D7)⋊C4, D4×C7⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14608);