Finite Group DatabasebetaFinite Group Databasebeta| order | 11132 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(Dic23⋊C11) |
| unambiguous semidirect product | (C23⋊C11)⋊Dic11 |
| unambiguous semidirect product | Dic253⋊C11 |
| derived | C11×C23 ⋊ C4×C11 |
| Hall | C11×C23⋊C11 ⋊ C4 |
| Sylow | C23 ⋊ C11×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊AGL(1,𝔽23) |
| commutator, hypocenter | C11×C23 | C4×C11 |
| Fitting, socle, cosocle | C2×C11×C23 | C2×C11 |
| prime radical | C2×C11×C23⋊C11 | C2 |
| LCS | G ▷ C11×C23 | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2,11^2,23,2|a^2=e,c^a=c^10,d^a=d^22,d^b=d^2176 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C11⋊(Dic23⋊C11), C3⋊(C11⋊(Dic23⋊C11)) |
| maximal normal subgroup of | C3×C11⋊(Dic23⋊C11) |
| maximal quotient of | C3×C11⋊(Dic23⋊C11), C3⋊(C11⋊(Dic23⋊C11)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11132, 16);