Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C491 ⋊ C2 |
| Sylow | C491 ⋊ #131 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
Polycyclic presentation:
2^5,491|a^2=d,d^2=e,c^b=ce,f^c=f^4903940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536508, #44536510, #44536840, … |
| maximal normal subgroup of | #44536508, #44536510, #44536840, … |
| maximal quotient of | #44536679, #44536680, #44536690, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 152);