Finite Group DatabasebetaFinite Group Databasebeta| order | 30612 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C2551⋊C3)⋊C4 |
| unambiguous semidirect product | Dic2551⋊C3 |
| derived, Sylow | C2551 ⋊ C3×C4 |
| Hall | Dic2551 ⋊ C3 |
| Hall | C2551⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2551⋊C3 |
| commutator, hypocenter | C2551 | C3×C4 |
| Fitting, socle, cosocle | C2×C2551 | C2×C3 |
| prime radical | C2×C2551⋊C3 | C2 |
| LCS | G ▷ C2551 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10204 |
Polycyclic presentation:
2,3,2551,2|a^2=d,c^a=c^2550,c^b=c^50862 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30612, 2);