Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q16×C491 ⋊ C2 |
| Sylow | C491 ⋊ SD32 |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
Polycyclic presentation:
2^5,491|a^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,c^b=cd,d^b=de,f^b=f^4901726 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD32×D491, C2×#30628280, #44537155, … |
| maximal normal subgroup of | SD32×D491, C2×#30628280, #44537155, … |
| maximal quotient of | #44536525, #44536529, #44536552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 89);