Finite Group DatabasebetaFinite Group Databasebeta| order | 18135 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C3×#11925882⋊C5 |
| unambiguous semidirect product | (C3×#11925882)⋊C5 |
| Fitting, socle | C3×C13×C31 ⋊ C3×C5 |
| derived, Hall | C13×C31 ⋊ C32×C5 |
| Hall | C3×#11925882 ⋊ C5 |
| Hall | C13×ΓL(1,𝔽32) ⋊ C32 |
| Hall | ΓL(1,𝔽32) ⋊ C3×C13⋊C3 |
| Sylow | C31 ⋊ C3×C5×C13⋊C3 |
| Sylow | C13 ⋊ C3×(C31⋊C3)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #11925882⋊C5 |
| commutator, cosocle, hypocenter | C13×C31 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C31 | C3×C5 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1209 |
183 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#14559030⋊C5, C3×#14559026⋊C5, C3×#14559022⋊C5, … |
| maximal normal subgroup of | C3×#14559030⋊C5, C3×#14559026⋊C5, C3×#14559022⋊C5, … |
| maximal quotient of | C2×C3×#11925882⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18135, 15);