Finite Group DatabasebetaFinite Group Databasebeta| order | 18135 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16813768⋊C5 |
| derived, Hall | C13×C31 ⋊ C5×C9 |
| Hall | #16813768 ⋊ C5 |
| Hall | C13×ΓL(1,𝔽32) ⋊ C9 |
| Hall | ΓL(1,𝔽32) ⋊ C13⋊C9 |
| Sylow | C31 ⋊ C5×C13⋊C9 |
| Sylow | C13 ⋊ ΓL(1,𝔽32)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #11925882⋊C5 |
| 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 |
Polycyclic presentation:
3,5,13,31,3|a^3=e,c^a=c^3,d^a=d^25,d^b=d^16183 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#16813768⋊C5, #20299821⋊C5, #20299825⋊C5, … |
| maximal normal subgroup of | C2×#16813768⋊C5, #20299821⋊C5, #20299825⋊C5, … |
| maximal quotient of | C2×#16813768⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18135, 9);