Finite Group DatabasebetaFinite Group Databasebeta| order | 10256 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C641 ⋊ C2 |
| Sylow | C641 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D641 |
| commutator, cosocle | C4×C641 | C22 |
| Frattini | C4 | C2×D641 |
| Fitting | D4×C641 | C2 |
| socle | C2×C641 | D4 |
| hypercenter | D4 | D641 |
| hypocenter | C641 | D8 |
| LCS | G ▷ C4×C641 ▷ C2×C641 ▷ C641 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
22 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,641|c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^6401607 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D8×D641, C2×#23779642, #35206370, … |
| maximal normal subgroup of | D8×D641, C2×#23779642, #35206370, … |
| maximal quotient of | #35206270, #35206271, #35206283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10256, 25);