Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #4177⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C32 |
| direct product | C4×#4177⋊C3 |
| unambiguous semidirect product | (C4×#4177)⋊C3 |
| Fitting | C4×#6910 ⋊ C2 |
| derived | C3×C9 ⋊ C2×C32×C4 |
| Sylow | #6910 ⋊ C2×C4 |
284 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | C4×(#4169⋊C3)⋊C3, C4×(#4176⋊C2)⋊C3, D4×#4177⋊C3, … |
| maximal normal subgroup of | C4×(#4169⋊C3)⋊C3, C4×(#4176⋊C2)⋊C3, D4×#4177⋊C3, … |
| maximal quotient of | AGL(1,𝔽5)×#4177⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1783);