Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊#4183 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×C3⋊#66330 |
| unambiguous semidirect product | (C2×C3)⋊#66330 |
| derived, Sylow | C3×AΣL(1,𝔽27) ⋊ C2×C4 |
843 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 843 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2153);