Finite Group DatabasebetaFinite Group Databasebeta| order | 3753 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×C139⋊C9 |
| unambiguous semidirect product | (C3×C139)⋊C9 |
| derived, Sylow | C139 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C139⋊C3 |
| commutator, hypocenter | C139 | C3×C9 |
| Frattini | C3 | C3×C139⋊C3 |
| Fitting, socle, prime radical | C32×C139 | C3 |
| cosocle | C3×C139 | C32 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C32 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3753 |
441 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C139⋊C9, (C3×C139⋊C3)⋊C9, C32⋊(C139⋊C9), … |
| maximal normal subgroup of | C9×C139⋊C9, (C3×C139⋊C3)⋊C9, C32⋊(C139⋊C9), … |
| maximal quotient of | C9×C139⋊C9, C32⋊(C139⋊C9), #26014603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3753, 8);