Finite Group DatabasebetaFinite Group Databasebeta| order | 1936 |
| isoclinism | isoclinic class of D121 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C121⋊C16 |
| derived, Sylow | C121 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D121 |
| commutator, hypocenter | C121 | C16 |
| Frattini | C8×C11 | D11 |
| Fitting, cosocle | C8×C121 | C2 |
| socle, prime radical | C2×C11 | C11⋊C8 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C8 | |
15 conjugacy classes of subgroups.
| minimal degree | μ(G) = 137 |
| transitive degree | μt(G) = 1936 |
Polycyclic presentation:
2^4,11^2|a^2=b,b^2=c,c^2=d,e^11=f,e^a=e^10f^10,f^a=f^10496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1936, 1);