Finite Group DatabasebetaFinite Group Databasebeta| order | 15728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C983 ⋊ M16 |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7864 |
Polycyclic presentation:
2^4,983|a^2=c,c^2=d,b^a=bd,e^a=e^9823938 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44537879, #44537880, #44537881, … |
| maximal normal subgroup of | #44537879, #44537880, #44537881, … |
| maximal quotient of | #44537874, C22⋊(C983⋊C8), C4⋊(C983⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15728, 24);