Finite Group DatabasebetaFinite Group Databasebeta| order | 1936 |
| isoclinism | isoclinic class of #11757263 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C11 |
| direct product | C2×#11757263 |
| Fitting, socle | C2×C112 ⋊ Q8 |
| Sylow | C112 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11757263 |
| commutator, cosocle | C11⋊D11 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C112 | Q8 |
| prime radical | C2×C11⋊D11 | C22 |
| hypocenter | C112 | C2×Q8 |
| LCS | G ▷ C11⋊D11 ▷ C112 | |
| UCS | C1 ◁ C2 | |
53 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
40 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1936, 162);