Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D27⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| direct product | C4×#6864⋊C2 |
| Fitting | C4×#6864 ⋊ C2 |
| derived | C27 ⋊ C2×C4×C9 |
| Sylow | #6864 ⋊ C2×C4 |
123 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 123 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 328);