Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | (C3⋊D3)⋊A4 |
| commutator, hypocenter | C22×H(3,𝔽3) | C2×C9 |
| Frattini | C3×C9 | D3×A4 |
| Fitting, cosocle | C22×#737 | C2×C3 |
| socle | C22×C3 | (C3⋊D3)⋊C9 |
| prime radical | C22×#272 | C9 |
| LCS | G ▷ C22×H(3,𝔽3) | |
| UCS | C1 ◁ C9 | |
144 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
2,3^2,2^2,3^3|b^3=c,c^3=h,f^a=f^2,g^a=g^2h,d^b=de,e^b=d,f^b=fg,g^f=gh96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 933);