Finite Group DatabasebetaFinite Group Databasebeta| order | 18135 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C9×ΓL(1,𝔽32) |
| unambiguous semidirect product | C13⋊(C9×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C31×C13⋊C9)⋊C5 |
| derived, Hall | C13×C31 ⋊ C5×C9 |
| Hall | C31×C13⋊C9 ⋊ C5 |
| Hall | C13×ΓL(1,𝔽32) ⋊ C9 |
| Sylow | C31 ⋊ C5×C13⋊C9 |
| Sylow | C13 ⋊ C9×ΓL(1,𝔽32) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C13⋊C3×ΓL(1,𝔽32) |
| commutator, hypocenter | C13×C31 | C5×C9 |
| Fitting, socle, cosocle | C3×C13×C31 | C3×C5 |
| prime radical | C3×C13×ΓL(1,𝔽32) | C3 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3627 |
231 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C13⋊C9×ΓL(1,𝔽32), C13⋊C9×D31⋊C5, ΓL(1,𝔽32)×D13⋊C9, … |
| maximal normal subgroup of | C2×C13⋊C9×ΓL(1,𝔽32), C13⋊C9×D31⋊C5, ΓL(1,𝔽32)×D13⋊C9, … |
| maximal quotient of | C2×C13⋊C9×ΓL(1,𝔽32) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18135, 8);