Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C491 ⋊ #97 |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15712 |
Polycyclic presentation:
2^5,491|a^2=c,b^2=d,c^2=e,b^a=be,f^b=f^4903940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536502, #97×D491, C2×#30628247, … |
| maximal normal subgroup of | #44536502, #97×D491, C2×#30628247, … |
| maximal quotient of | #44536446, #44536447, #44536479, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 56);