Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M16×C491 ⋊ C2 |
| Sylow | C491 ⋊ #100 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3928 |
Polycyclic presentation:
2^5,491|a^2=d,d^2=e,b^a=bc,c^a=ce,d^b=de,f^b=f^4902461 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #100×D491, C2×#30628253, #44536707, … |
| maximal normal subgroup of | #100×D491, C2×#30628253, #44536707, … |
| maximal quotient of | #44536448, #44536464, #44536468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 62);