Finite Group DatabasebetaFinite Group Databasebeta| order | 15728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D983)⋊C4 |
| Fitting | C2×C4×C983 ⋊ C2 |
| Sylow | C983 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7864 |
Polycyclic presentation:
2^4,983|a^2=d,b^a=bc,e^b=e^9823938 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D983, C2×(C2×D983)⋊C4, #44537920, … |
| maximal normal subgroup of | C22⋊C4×D983, C2×(C2×D983)⋊C4, #44537920, … |
| maximal quotient of | C983⋊#95, (C2×D983)⋊C8, #44537877, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15728, 17);