Finite Group DatabasebetaFinite Group Databasebeta| order | 1936 |
| isoclinism | isoclinic class of D121 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×D121 |
| unambiguous semidirect product | C121⋊C24 |
| unambiguous semidirect product | (C2×C121)⋊C23 |
| Fitting | C23×C121 ⋊ C2 |
| derived, Sylow | C121 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D121 |
| commutator, cosocle, hypocenter | C121 | C24 |
| Frattini | C11 | C23×D11 |
| Fitting | C23×C121 | C2 |
| socle | C23×C11 | D11 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C23 | |
201 conjugacy classes of subgroups.
| transitive degree | μt(G) = 968 |
496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1936, 41);