Finite Group DatabasebetaFinite Group Databasebeta| order | 10264 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1283⋊C8 |
| derived, Sylow | C1283 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D1283 |
| commutator, hypocenter | C1283 | C8 |
| Fitting, cosocle | C4×C1283 | C2 |
| socle, prime radical | C2×C1283 | C4 |
| LCS | G ▷ C1283 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1283|a^2=b,b^2=c,d^a=d^12822572 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D1283, C2×C1283⋊C8, #35206535, … |
| maximal normal subgroup of | C8×D1283, C2×C1283⋊C8, #35206535, … |
| maximal quotient of | C1283⋊C16, C2×C1283⋊C8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10264, 6);