Finite Group DatabasebetaFinite Group Databasebeta| order | 18135 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C3×C5×#11925882 |
| Fitting, socle | C3×C5×C13×C31 ⋊ C3 |
| derived, Hall | C13×C31 ⋊ C32×C5 |
| Hall | C5×C13×C31 ⋊ C32 |
| Hall | C5×C31 ⋊ C3×C13⋊C3 |
| Hall | C5×C13 ⋊ C3×C31⋊C3 |
| Sylow | C31 ⋊ C3×C5×C13⋊C3 |
| Sylow | C13 ⋊ C3×C5×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | #11925882 |
| commutator, cosocle, hypocenter | C13×C31 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C13×C31 | C3 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 ◁ C3×C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6045 |
2055 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×#14559030, C3×C5×#14559026, C3×C5×#14559022, … |
| maximal normal subgroup of | C3×C5×#14559030, C3×C5×#14559026, C3×C5×#14559022, … |
| maximal quotient of | C2×C3×C5×#11925882 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18135, 20);