Finite Group DatabasebetaFinite Group Databasebeta| order | 12210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C37⋊AGL(1,𝔽11)) |
| unambiguous semidirect product | C37⋊(C3⋊AGL(1,𝔽11)) |
| unambiguous semidirect product | (C11⋊C5)⋊D111 |
| unambiguous semidirect product | D1221⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C37 | C2×C5 |
| LCS | G ▷ C3×C11×C37 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,11,37|b^a=b^2,d^a=d^10,e^a=e^36,d^c=d^4396 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12210, 26);