Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C491 ⋊ C2 |
| Sylow | C491 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3928 |
Polycyclic presentation:
2^5,491|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^490,d^b=de,f^c=f^4901726 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,ℤ/8)×D491, C2×#30628364, #44537522, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×D491, C2×#30628364, #44537522, … |
| maximal quotient of | #44536725, #44536728, #44536764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 173);