Finite Group DatabasebetaFinite Group Databasebeta| order | 12012 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#11763957 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊#10587716 |
| commutator, hypocenter | C7×C11×C13 | C3×C4 |
| Fitting, socle, cosocle | C2×C7×C11×C13 | C2×C3 |
| prime radical | C2×C11×#63270 | C2 |
| LCS | G ▷ C7×C11×C13 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,11,13,2|a^2=f,d^a=d^10,e^a=e^12,c^b=c^2,e^b=e^3378 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12012, 31);