Finite Group DatabasebetaFinite Group Databasebeta| order | 1332 |
| isoclinism | isoclinic class of C22⋊(C37⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C22⋊(C37⋊C3) |
| unambiguous semidirect product | (C22×C3)⋊(C37⋊C3) |
| unambiguous semidirect product | (C3×C37)⋊A4 |
| Fitting, socle | C22×C3×C37 ⋊ C3 |
| derived, Hall | C22×C37 ⋊ C32 |
| Sylow | C37 ⋊ C3×A4 |
| Sylow | C22 ⋊ C3×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C22⋊(C37⋊C3) |
| commutator, cosocle, hypocenter | C22×C37 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C37 | C3 |
| LCS | G ▷ C22×C37 | |
| UCS | C1 ◁ C3 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 444 |
156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1332, 55);