Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #4175 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C9 · Schur multiplier (H2) = C3 |
No aliases for this group.
| derived | C33 ⋊ C8×C9 |
| Sylow | #6866 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | #4175 |
| commutator, hypocenter | C33 | C8×C9 |
| Frattini | C33×C4 | C3×D3 |
| Fitting | C4×#6866 | C2 |
| socle | C2×C32 | (C3⋊Dic3)⋊C3 |
| prime radical | C2×C34 | C3×C4 |
| cosocle | C34×C4 | C2×C3 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C3×C4 | |
205 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 205 conjugacy classes of subgroups — too many to draw. Only its 33 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:
2,3,2,3,2,3^3|a^2=c,b^3=d,c^2=e,f^a=f^2,g^a=g^2,h^a=h^2,f^b=fg,g^b=gh156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 27);