Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×#10619994 |
| Fitting | C22×C32×H(3,𝔽3) ⋊ C2 |
| Sylow | C32×H(3,𝔽3) ⋊ D4 |
1829 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 1829 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | #72229150, #72259736, #72259785, … |
| maximal normal subgroup of | #72259736, #72259785, C3×#13048731 |
| maximal quotient of | #72229150 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3394);