Finite Group DatabasebetaFinite Group Databasebeta| order | 10256 |
| automorphism | Aut(G) order 13127680 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2564 |
| Sylow | C641 ⋊ Q16 |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,641|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^640,c^b=cd,e^b=e^6402567 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35206294, #35206295, #35206296, … |
| maximal normal subgroup of | #35206294, #35206295, #35206296, … |
| maximal quotient of | #35206275, #35206284, C2×Dic2564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10256, 31);