Finite Group DatabasebetaFinite Group Databasebeta| order | 5536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊#10621924 |
| unambiguous semidirect product | D173⋊(C4⋊C4) |
| Fitting | C2×C4×C173 ⋊ C4 |
| Sylow | C173 ⋊ C2×C4⋊C4 |
92 conjugacy classes of subgroups.
364 conjugacy classes — view the full character table.
| maximal subgroup of | #26012364, #26012365, #26012370, … |
| maximal normal subgroup of | #26012364, #26012365, #26012370, … |
| maximal quotient of | C2×(C2×#10621924)⋊C4, C4×C4⋊#10621924, #26012433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5536, 224);