Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C35 |
| unambiguous semidirect product | C4⋊(C3⋊(C3⋊#272)) |
| Fitting | C32×C4×H(3,𝔽3) ⋊ C2 |
| Sylow | C32×H(3,𝔽3) ⋊ D4 |
2664 conjugacy classes of subgroups; only the 657 normal subgroups are shown.
This group has 2664 conjugacy classes of subgroups — too many to draw. Only its 657 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^3,3^5|b^2=c,b^a=bc,d^a=d^2,e^a=e^2,f^a=f^2,g^a=g^2,g^f=gh207 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3406);