Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16838652⋊C3 |
| Fitting, socle, derived, Sylow | C312 ⋊ C3×C4 |
| Hall | #16838652 ⋊ C3 |
| Hall | #15668332 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C312 | C3×C4 |
| prime radical | #19153443 | C2 |
| cosocle | C31⋊D31 | C2×C3 |
| LCS | G ▷ C312 | |
| UCS | C1 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,31^2|a^2=c,d^a=d^19e^13,e^a=d^27e^12,d^b=d^25,e^b=e^25,d^c=d^30,e^c=e^3092 conjugacy classes — view the full character table.
| maximal subgroup of | #26040355⋊C3, C3×#16838652⋊C3, C3⋊(#16838652⋊C3) |
| maximal normal subgroup of | C3×#16838652⋊C3 |
| maximal quotient of | #16838652⋊C9, C3×#16838652⋊C3, C3⋊(#16838652⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 39);