Finite Group DatabasebetaFinite Group Databasebeta| order | 1936 |
| isoclinism | isoclinic class of C11⋊D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊(C11⋊C16) |
| derived, Sylow | C112 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | C11⋊D11 |
| commutator, hypocenter | C112 | C16 |
| Fitting, cosocle | C8×C112 | C2 |
| socle, prime radical | C2×C112 | C8 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C8 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1936 |
Polycyclic presentation:
2^4,11^2|a^2=b,b^2=c,c^2=d,e^a=e^10,f^a=f^10496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1936, 44);