Finite Group DatabasebetaFinite Group Databasebeta| order | 1936 |
| isoclinism | isoclinic class of D112 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | Dic112 |
| derived, Sylow | C112 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D112 |
| commutator, hypocenter | C112 | C42 |
| Fitting, socle, prime radical, cosocle | C22×C112 | C22 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C22 | |
100 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, 58);