Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C4×#92394 |
| Fitting | C4×3−1+4 ⋊ C2 |
| Sylow | 3−1+4 ⋊ C2×C4 |
644 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#13091119, C4×(#4207⋊C2)⋊C3, D4×#92394, … |
| maximal normal subgroup of | C4×(#4207⋊C2)⋊C3, D4×#92394, #72259352 |
| maximal quotient of | AGL(1,𝔽5)×#92394 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3338);