Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C32 |
| direct product | C4×#92300 |
| Fitting | C4×C32⋊H(3,𝔽3) ⋊ C2 |
| derived | C3×H(3,𝔽3) ⋊ C2×C3×C4 |
| Sylow | C32⋊H(3,𝔽3) ⋊ C2×C4 |
706 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 706 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×#92300, C4×#11757730, … |
| maximal normal subgroup of | D4×#92300, C4×#11757730, #72259895 |
| maximal quotient of | C4×#13091119, AGL(1,𝔽5)×#92300 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1916);