Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C491 ⋊ #107 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15712 |
Polycyclic presentation:
2^5,491|a^2=d,b^2=ce,c^2=e,b^a=bc,c^a=ce,f^b=f^4902464 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #107×D491, C2×#30628270, #44536760, … |
| maximal normal subgroup of | #107×D491, C2×#30628270, #44536760, … |
| maximal quotient of | #44536477, #44536487, #44536550, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 79);