Finite Group DatabasebetaFinite Group Databasebeta| order | 1776 |
| isoclinism | isoclinic class of C22⋊(C37⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×C22⋊(C37⋊C3) |
| unambiguous semidirect product | (C22×C4)⋊(C37⋊C3) |
| unambiguous semidirect product | (C4×C37)⋊A4 |
| Fitting, Hall | C22×C4×C37 ⋊ C3 |
| derived | C22×C37 ⋊ C3×C4 |
| Sylow | C37 ⋊ C4×A4 |
| Sylow | C22×C4 ⋊ C37⋊C3 |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 444 |
208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1776, 201);