Finite Group DatabasebetaFinite Group Databasebeta| order | 36410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D331⋊C11) |
| unambiguous semidirect product | D1655⋊C11 |
| unambiguous semidirect product | (C331⋊C11)⋊D5 |
| Fitting, socle, derived, Hall | C5×C331 ⋊ C2×C11 |
| Hall | C5×C331⋊C11 ⋊ C2 |
| Hall | C331⋊C11 ⋊ D5 |
| Hall | D1655 ⋊ C11 |
| Sylow | C331 ⋊ D5×C11 |
| Sylow | C5 ⋊ D331⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C331 | C2×C11 |
| LCS | G ▷ C5×C331 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1655 |
Polycyclic presentation:
2,5,11,331|b^a=b^4,d^a=d^330,d^c=d^270119 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36410, 19);