Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C491 ⋊ M32 |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
Polycyclic presentation:
2^5,491|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^4903940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536502, #44536503, #44536506, … |
| maximal normal subgroup of | #44536502, #44536503, #44536506, … |
| maximal quotient of | #44536501, C22⋊(C491⋊C16), C4⋊(C491⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 86);