Finite Group DatabasebetaFinite Group Databasebeta| order | 3756 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×D313⋊C3 |
| unambiguous semidirect product | D313⋊(C2×C3) |
| unambiguous semidirect product | (C313⋊C3)⋊C22 |
| unambiguous semidirect product | (C2×D313)⋊C3 |
| unambiguous semidirect product | (C2×C313⋊C3)⋊C2 |
| Fitting, socle | C2×C313 ⋊ C2×C3 |
| derived, Sylow | C313 ⋊ C22×C3 |
| Hall | C2×D313 ⋊ C3 |
| Hall | C313⋊C3 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D313⋊C3 |
| commutator, cosocle, hypocenter | C313 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C313 | C2×C3 |
| LCS | G ▷ C313 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 626 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D313⋊C3, C2×C3×D313⋊C3, C2×C3⋊(D313⋊C3), … |
| maximal normal subgroup of | C2×C3×D313⋊C3, C2×C5×D313⋊C3, C2×C7×D313⋊C3 |
| maximal quotient of | C2×D313⋊C9, D3×D313⋊C3, C2×C3×D313⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3756, 9);