Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C4×#92338 |
| Fitting | C4×C32⋊H(3,𝔽3) ⋊ C2 |
| derived, Sylow | C32⋊H(3,𝔽3) ⋊ C2×C4 |
1031 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 1031 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | D4×#92338, C4×#13091119, C4×#11757730, … |
| maximal normal subgroup of | D4×#92338, C4×#13091119, C4×#11757730, … |
| maximal quotient of | C4×#13091120, AGL(1,𝔽5)×#92338 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2123);