Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D491)⋊C8 |
| Fitting | C2×C8×C491 ⋊ C2 |
| Sylow | C491 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
Polycyclic presentation:
2^5,491|a^2=d,d^2=e,b^a=bc,f^b=f^4903940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C8×D491, C2×(C2×D491)⋊C8, #44536687, … |
| maximal normal subgroup of | C22⋊C8×D491, C2×(C2×D491)⋊C8, #44536687, … |
| maximal quotient of | #44536448, #44536450, #44536452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 58);