Finite Group DatabasebetaFinite Group Databasebeta| order | 1936 |
| isoclinism | isoclinic class of D112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×D11×Dic11 |
| derived, Sylow | C112 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D112 |
| commutator, hypocenter | C112 | C22×C4 |
| Frattini | C2 | C2×D112 |
| Fitting, socle | C22×C112 | C22 |
| prime radical | C22×C11×D11 | C2 |
| cosocle | C2×C112 | C23 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C22 | |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1936, 126);