Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C491 ⋊ #102 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
Polycyclic presentation:
2^5,491|a^2=d,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 | #102×D491, C2×#30628258, #44536718, … |
| maximal normal subgroup of | #102×D491, C2×#30628258, #44536718, … |
| maximal quotient of | D4⋊(C491⋊C8), #44536459, #44536469, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 67);