Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2×C31 |
| unambiguous semidirect product | C22⋊#15668333 |
| Fitting, socle, derived, Hall | C22×C312 ⋊ C3 |
| Sylow | C312 ⋊ A4 |
| Sylow | C22 ⋊ #15668333 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C312 | C3 |
| LCS | G ▷ C22×C312 | |
| UCS | C1 | |
70 conjugacy classes of subgroups.
Polycyclic presentation:
3,2^2,31^2|b^a=c,c^a=bc,d^a=d^5,e^a=e^251284 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C31⋊C3×C22⋊(C31⋊C3), #15668332⋊A4, A4×#15668333, … |
| maximal normal subgroup of | C31⋊C3×C22⋊(C31⋊C3), #15668332⋊A4, A4×#15668333, … |
| maximal quotient of | C22⋊#22575711, C3×C22⋊#15668333 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 55);