Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C491 ⋊ #103 |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15712 |
Polycyclic presentation:
2^5,491|a^2=d,b^2=e,c^2=e,b^a=bc,c^a=ce,f^a=f^490,c^b=ce2464 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #103×D491, C2×#30628261, #44536720, … |
| maximal normal subgroup of | #103×D491, C2×#30628261, #44536720, … |
| maximal quotient of | Q8⋊(C491⋊C8), #44536462, #44536471, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 70);