Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | #10619884⋊C3 |
| Sylow | C32⋊H(3,𝔽3) ⋊ D4 |
402 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^2,3,2,3^4|b^a=bd,f^a=f^2,g^a=g^2,h^a=h^2,e^b=e^2,h^b=h^2,f^c=fg,f^e=fh69 conjugacy classes — view the full character table.
| maximal subgroup of | #72219705, #72219727, #72219730, … |
| maximal normal subgroup of | #72219705, #72219727, #72219730 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1198);