Finite Group DatabasebetaFinite Group Databasebeta| order | 36905 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×C121⋊C5 |
| unambiguous semidirect product | C121⋊(C5×C61) |
| Fitting, Hall | C61×C121 ⋊ C5 |
| derived, Sylow | C121 ⋊ C5×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | C121⋊C5 |
| commutator, cosocle, hypocenter | C121 | C5×C61 |
| Frattini | C11 | C11⋊C5×C61 |
| Fitting | C61×C121 | C5 |
| socle | C11×C61 | C11⋊C5 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C61 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7381 |
1769 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36905, 2);