Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C312 ⋊ C3×C4 |
| Hall | C31×Dic31 ⋊ C3 |
| Hall | #15668332 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #19153445 |
| commutator, hypocenter | C312 | C3×C4 |
| Fitting, socle, cosocle | C2×C312 | C2×C3 |
| prime radical | C2×#15668332 | C2 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C2 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,31^2,2|a^2=e,c^a=c^30,c^b=c^5,d^b=d^5362 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×(C31⋊C3)⋊C4, #26040341⋊C3, C3×#26040337, … |
| maximal normal subgroup of | C31⋊C3×(C31⋊C3)⋊C4, C3×#26040337 |
| maximal quotient of | #46829291, C3×#26040337, C3⋊#26040337 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 20);