Finite Group DatabasebetaFinite Group Databasebeta| order | 15728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q8×C983 ⋊ C2 |
| Sylow | C983 ⋊ SD16 |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7864 |
Polycyclic presentation:
2^4,983|a^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^9822462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×D983, C2×#30628462, #44537983, … |
| maximal normal subgroup of | SD16×D983, C2×#30628462, #44537983, … |
| maximal quotient of | #44537883, #44537887, #44537894, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15728, 27);