Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #92302 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×#92302 |
| Fitting | C4×#6891 ⋊ C2 |
| derived | C32⋊C9 ⋊ C2×C3×C4 |
| Sylow | #6891 ⋊ C2×C4 |
553 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 553 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#13091120, D4×#92302, C4×(((C3⋊D3)⋊C9)⋊C2)⋊C3, … |
| maximal normal subgroup of | D4×#92302, C4×(((C3⋊D3)⋊C9)⋊C2)⋊C3, #72259306 |
| maximal quotient of | AGL(1,𝔽5)×#92302 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1921);