Finite Group DatabasebetaFinite Group Databasebeta| order | 11220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D51⋊AGL(1,𝔽11) |
| unambiguous semidirect product | (C3⋊AGL(1,𝔽11))⋊D17 |
| unambiguous semidirect product | (C17⋊AGL(1,𝔽11))⋊D3 |
| unambiguous semidirect product | (D33⋊D17)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C17 | C22×C5 |
| LCS | G ▷ C3×C11×C17 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,3,11,17|e^a=e^10,f^a=f^16,d^b=d^2,e^b=e^10,e^c=e^4177 conjugacy classes — view the full character table.
| maximal subgroup of | D153⋊AGL(1,𝔽11), C3×D51⋊AGL(1,𝔽11), D51⋊(C3⋊AGL(1,𝔽11)), … |
| maximal normal subgroup of | C3×D51⋊AGL(1,𝔽11) |
| maximal quotient of | D153⋊AGL(1,𝔽11), C3×D51⋊AGL(1,𝔽11), D51⋊(C3⋊AGL(1,𝔽11)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11220, 34);