Finite Group DatabasebetaFinite Group Databasebeta| order | 10256 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C641 ⋊ C2 |
| Sylow | C641 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D641 |
| commutator, socle, cosocle | C2×C641 | C23 |
| Fitting | Q8×C641 | C2 |
| hypercenter | Q8 | D641 |
| hypocenter | C641 | #41 |
| LCS | G ▷ C2×C641 ▷ C641 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,641|c^2=d,b^a=bd,e^a=e^640,e^b=e^640,e^c=e^6401610 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35206371, #35206373, #35206377, … |
| maximal normal subgroup of | #35206371, #35206373, #35206377, … |
| maximal quotient of | #35206308, #35206312, Q8×Dic641, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10256, 41);