Finite Group DatabasebetaFinite Group Databasebeta| order | 10256 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×C22⋊D641 |
| unambiguous semidirect product | C23⋊D641 |
| Fitting | C23×C641 ⋊ C2 |
| Sylow | C641 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D641 |
| commutator, cosocle | C2×C641 | C23 |
| Frattini | C2 | C22×D641 |
| Fitting | C23×C641 | C2 |
| socle | C22×C641 | C22 |
| hypercenter | C23 | D641 |
| hypocenter | C641 | C2×D4 |
| LCS | G ▷ C2×C641 ▷ C641 | |
| UCS | C1 ◁ C22 ◁ C23 | |
54 conjugacy classes of subgroups.
2570 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35206264, #35206310, C4×C22⋊D641, … |
| maximal normal subgroup of | #35206264, #35206310, C4×C22⋊D641, … |
| maximal quotient of | C2×#23779634, C2×C22⋊Dic641, C2×#23779636, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10256, 35);