Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C22⋊C4×C491 ⋊ C2 |
| Sylow | C491 ⋊ #124 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
Polycyclic presentation:
2^5,491|b^2=e,c^2=d,b^a=bd,c^a=ce,f^c=f^4902464 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #124×D491, C2×#30628323, #44537252, … |
| maximal normal subgroup of | #124×D491, C2×#30628323, #44537252, … |
| maximal quotient of | #44536589, #44536613, #44536614, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 132);