Finite Group DatabasebetaFinite Group Databasebeta| order | 1332 |
| isoclinism | isoclinic class of C22⋊(C37⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#66524 |
| derived, Hall | C22×C37 ⋊ C9 |
| Sylow | C37 ⋊ C22⋊C9 |
| Sylow | C22 ⋊ #66524 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊(C37⋊C3) |
| commutator, hypocenter | C22×C37 | C9 |
| Fitting, socle, prime radical, cosocle | C22×C3×C37 | C3 |
| LCS | G ▷ C22×C37 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 50 |
| transitive degree | μt(G) = 666 |
Polycyclic presentation:
3^2,2^2,37|a^3=b,c^a=cd,d^a=c,e^a=e^10156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1332, 14);