Finite Group DatabasebetaFinite Group Databasebeta| order | 10256 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C641 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C641 | C16 |
| prime radical | D641 | C8 |
| cosocle | #19104063 | C2 |
| LCS | G ▷ C641 | |
| UCS | C1 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,641|a^2=b,b^2=c,c^2=d,e^a=e^601,e^b=e^318,e^c=e^487,e^d=e^64056 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#23779671, #35206451 |
| maximal normal subgroup of | C2×#23779671, #35206451 |
| maximal quotient of | #35206449, C2×#23779671 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10256, 54);