Finite Group DatabasebetaFinite Group Databasebeta| order | 18990 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D5×C211⋊C9 |
| unambiguous semidirect product | C5⋊(C2×C211⋊C9) |
| unambiguous semidirect product | (D5×C211)⋊C9 |
| derived, Hall | C5×C211 ⋊ C2×C9 |
| Hall | C5×C211⋊C9 ⋊ C2 |
| Hall | D5×C211 ⋊ C9 |
| Sylow | C211 ⋊ C9×D5 |
| Sylow | C5 ⋊ C2×C211⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D5×C211⋊C3 |
| commutator, hypocenter | C5×C211 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C211 | C2×C3 |
| prime radical | C3×D5×C211 | C3 |
| LCS | G ▷ C5×C211 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9495 |
876 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C211⋊C9)⋊AGL(1,𝔽5), AGL(1,𝔽5)×C211⋊C9, D5×D211⋊C9, … |
| maximal normal subgroup of | (C211⋊C9)⋊AGL(1,𝔽5), AGL(1,𝔽5)×C211⋊C9, D5×D211⋊C9, … |
| maximal quotient of | Dic5×C211⋊C9, C2×D5×C211⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18990, 16);