Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #19153446⋊C2 |
| Fitting, socle, derived, Sylow | C312 ⋊ C22×C3 |
| Hall | D312 ⋊ C3 |
| Hall | #15668333 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C312 | C22×C3 |
| LCS | G ▷ C312 | |
| UCS | C1 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,31^2|e^a=e^30,d^b=d^30,d^c=d^5,e^c=e^25107 conjugacy classes — view the full character table.
| maximal subgroup of | D31⋊C32, C3×#19153446⋊C2, #19153446⋊D3, … |
| maximal normal subgroup of | D31⋊C32, C3×#19153446⋊C2 |
| maximal quotient of | #31772347⋊C2, C3×#19153446⋊C2, #19153446⋊D3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 35);