Finite Group DatabasebetaFinite Group Databasebeta| order | 36090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C2×C32×C401⋊C5 |
| unambiguous semidirect product | (C2×C401)⋊(C32×C5) |
| unambiguous semidirect product | (C2×C3×C401)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C32×C401)⋊C5 |
| Fitting, socle, Hall | C2×C32×C401 ⋊ C5 |
| derived, Sylow | C401 ⋊ C2×C32×C5 |
| Hall | C32×C401 ⋊ C2×C5 |
| Hall | C2×C401 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | C401⋊C5 |
| commutator, cosocle, hypocenter | C401 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C401 | C5 |
| LCS | G ▷ C401 | |
| UCS | C1 ◁ C2×C32 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7218 |
1530 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36090, 19);