Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C32 |
| direct product | C4×C9⋊#272 |
| Fitting | C4×C9×H(3,𝔽3) ⋊ C2 |
| derived, Sylow | C9×H(3,𝔽3) ⋊ C2×C4 |
678 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2120);