Finite Group DatabasebetaFinite Group Databasebeta| order | 36090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D3×C401⋊C5 |
| unambiguous semidirect product | C3⋊(D3×C401⋊C5) |
| unambiguous semidirect product | (C3⋊D3×C401)⋊C5 |
| Fitting, socle, derived, Hall | C32×C401 ⋊ C2×C5 |
| Hall | C32×C401⋊C5 ⋊ C2 |
| Hall | C3⋊D3×C401 ⋊ C5 |
| Sylow | C401 ⋊ C5×C3⋊D3 |
| Sylow | C32 ⋊ C2×C401⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C401 | C2×C5 |
| LCS | G ▷ C32×C401 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3609 |
510 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36090, 18);