Finite Group DatabasebetaFinite Group Databasebeta| order | 3753 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C32⋊(C139⋊C3) |
| unambiguous semidirect product | C139⋊H(3,𝔽3) |
| unambiguous semidirect product | (C3×C139⋊C3)⋊C3 |
| Fitting | C32×C139 ⋊ C3 |
| Sylow | C139 ⋊ H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C139⋊C3 |
| commutator, socle, cosocle | C3×C139 | C32 |
| Fitting | C32×C139 | C3 |
| hypercenter | C32 | C139⋊C3 |
| hypocenter | C139 | H(3,𝔽3) |
| LCS | G ▷ C3×C139 ▷ C139 | |
| UCS | C1 ◁ C3 ◁ C32 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1251 |
Polycyclic presentation:
3^3,139|b^a=bc,d^b=d^96425 conjugacy classes — view the full character table.
| maximal subgroup of | #26014611, #26014612, #26014614, … |
| maximal normal subgroup of | #26014611, #26014612, #26014614, … |
| maximal quotient of | (C3×C139⋊C3)⋊C9, C32⋊(C139⋊C9), #26014610, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3753, 9);