Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C491 ⋊ #99 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3928 |
Polycyclic presentation:
2^5,491|a^2=d,b^a=bc,c^a=ce,f^a=f^490,d^b=de2461 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536512, #44536513, #44536515, … |
| maximal normal subgroup of | #44536512, #44536513, #44536515, … |
| maximal quotient of | #44536449, #44536451, #44536459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 61);