Finite Group DatabasebetaFinite Group Databasebeta| order | 3753 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C9×C139 ⋊ C3 |
| Sylow | C139 ⋊ 3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C139⋊C3 |
| commutator, socle, cosocle | C3×C139 | C32 |
| Fitting | C9×C139 | C3 |
| prime radical | C3×C139⋊C3 | C3 |
| hypercenter | C9 | C139⋊C3 |
| hypocenter | C139 | 3−1+2 |
| LCS | G ▷ C3×C139 ▷ C139 | |
| UCS | C1 ◁ C3 ◁ C9 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1251 |
Polycyclic presentation:
3^3,139|a^3=c,b^a=bc,d^b=d^96425 conjugacy classes — view the full character table.
| maximal subgroup of | 3−1+2×C139⋊C3, C3×#16836728, #26014629, … |
| maximal normal subgroup of | 3−1+2×C139⋊C3, C3×#16836728, #26014629, … |
| maximal quotient of | (C3×C139⋊C3)⋊C9, (C139⋊C9)⋊C9, #26014604, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3753, 10);