Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#92265 |
| Fitting | C4×#6900 ⋊ C2 |
| Sylow | #6900 ⋊ D4 |
261 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^2,3^2,2,3^3|b^2=e,d^3=f,g^3=h,b^a=be,g^a=g^2h^2,h^a=h^2,d^c=df,g^c=gh135 conjugacy classes — view the full character table.
| maximal subgroup of | #72219871, #72219872, #72219876, … |
| maximal normal subgroup of | #72219871, #72219872, #72219876, … |
| maximal quotient of | #72219962 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1727);