Finite Group DatabasebetaFinite Group Databasebeta| order | 12612 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C1051⋊C3)⋊C4 |
| unambiguous semidirect product | Dic1051⋊C3 |
| derived, Sylow | C1051 ⋊ C3×C4 |
| Hall | Dic1051 ⋊ C3 |
| Hall | C1051⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1051⋊C3 |
| commutator, hypocenter | C1051 | C3×C4 |
| Fitting, socle, cosocle | C2×C1051 | C2×C3 |
| prime radical | C2×C1051⋊C3 | C2 |
| LCS | G ▷ C1051 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,1051,2|a^2=d,c^a=c^1050,c^b=c^870362 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(C1051⋊C3)⋊C4, C3⋊((C1051⋊C3)⋊C4) |
| maximal normal subgroup of | C3×(C1051⋊C3)⋊C4 |
| maximal quotient of | Dic1051⋊C9, C3×(C1051⋊C3)⋊C4, C3⋊((C1051⋊C3)⋊C4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12612, 2);