Finite Group DatabasebetaFinite Group Databasebeta| order | 3753 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C139⋊C27 |
| derived, Sylow | C139 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | C139⋊C3 |
| commutator, hypocenter | C139 | C27 |
| Fitting, cosocle | C9×C139 | C3 |
| socle, prime radical | C3×C139 | C9 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C9 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 166 |
| transitive degree | μt(G) = 3753 |
Polycyclic presentation:
3^3,139|a^3=b,b^3=c,d^a=d^96441 conjugacy classes — view the full character table.
| maximal subgroup of | C27×C139⋊C3, C3×C139⋊C27, #26014607, … |
| maximal normal subgroup of | C27×C139⋊C3, C3×C139⋊C27, #26014607, … |
| maximal quotient of | C139⋊C81, C3×C139⋊C27 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3753, 6);