Finite Group DatabasebetaFinite Group Databasebeta| order | 18135 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C13×C31 ⋊ C32×C5 |
| Hall | C13⋊C3×C31⋊C3 ⋊ 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, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C31 | C32×C5 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 403 |
119 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18135, 12);