Finite Group DatabasebetaFinite Group Databasebeta| order | 12468 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C1039⋊C3)⋊C4 |
| unambiguous semidirect product | Dic1039⋊C3 |
| derived, Sylow | C1039 ⋊ C3×C4 |
| Hall | Dic1039 ⋊ C3 |
| Hall | C1039⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1039⋊C3 |
| commutator, hypocenter | C1039 | C3×C4 |
| Fitting, socle, cosocle | C2×C1039 | C2×C3 |
| prime radical | C2×C1039⋊C3 | C2 |
| LCS | G ▷ C1039 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,1039,2|a^2=d,c^a=c^1038,c^b=c^140358 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(C1039⋊C3)⋊C4, C3⋊((C1039⋊C3)⋊C4) |
| maximal normal subgroup of | C3×(C1039⋊C3)⋊C4 |
| maximal quotient of | Dic1039⋊C9, C3×(C1039⋊C3)⋊C4, C3⋊((C1039⋊C3)⋊C4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12468, 2);