Finite Group DatabasebetaFinite Group Databasebeta| order | 36410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×D331⋊C11 |
| unambiguous semidirect product | (C5×D331)⋊C11 |
| Fitting, socle, Hall | C5×C331 ⋊ C2×C11 |
| derived, Sylow | C331 ⋊ C2×C5×C11 |
| Hall | C5×C331⋊C11 ⋊ C2 |
| Hall | C331⋊C11 ⋊ C2×C5 |
| Hall | C5×D331 ⋊ C11 |
| Hall | D331 ⋊ C5×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D331⋊C11 |
| commutator, cosocle, hypocenter | C331 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C331 | C2×C11 |
| LCS | G ▷ C331 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1655 |
185 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36410, 17);