Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C128 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊C128 |
| derived, Sylow | C11 ⋊ C128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C64 | D11 |
| commutator, hypocenter | C11 | C128 |
| Fitting, cosocle | C11×C64 | C2 |
| socle, prime radical | C2×C11 | C64 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C64 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 139 |
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^7,11|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^10448 conjugacy classes — view the full character table.
| maximal subgroup of | D11×C128, C2×C11⋊C128, #14641683, … |
| maximal normal subgroup of | D11×C128, C2×C11⋊C128, #14641683, … |
| maximal quotient of | C11⋊C256, C2×C11⋊C128 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2329);