Finite Group DatabasebetaFinite Group Databasebeta| order | 1926 |
| isoclinism | isoclinic class of C3⋊D321 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D321 |
| unambiguous semidirect product | C107⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C107 ⋊ C2 |
| Sylow | C107 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ D107 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C107 | C2 |
| LCS | G ▷ C32×C107 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 963 |
Polycyclic presentation:
2,3^2,107|b^a=b^2,c^a=c^2,d^a=d^106483 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×D107, D3×D321, C2×C3⋊D321, … |
| maximal normal subgroup of | C3⋊D3×D107, D3×D321, C2×C3⋊D321, … |
| maximal quotient of | C3⋊Dic321, C2×C3⋊D321, C3⋊D2247, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1926, 9);