Finite Group DatabasebetaFinite Group Databasebeta| order | 36355 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C661⋊C5)⋊C11 |
| unambiguous semidirect product | (C661⋊C11)⋊C5 |
| Fitting, socle, derived, Sylow | C661 ⋊ C5×C11 |
| Hall | C661⋊C11 ⋊ C5 |
| Hall | C661⋊C5 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C661 | C5×C11 |
| LCS | G ▷ C661 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 661 |
Polycyclic presentation:
5,11,661|c^a=c^247,c^b=c^63467 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36355, 1);