Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (3−1+2⋊C9)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (3−1+2⋊C9)⋊C8 |
| derived, Sylow | 3−1+2⋊C9 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | (3−1+2⋊C9)⋊C2 |
| commutator, hypocenter | 3−1+2⋊C9 | C8 |
| Frattini | C33×C4 | C3⋊D3 |
| Fitting, cosocle | C4×3−1+2⋊C9 | C2 |
| socle | C2×C32 | #1084 |
| prime radical | C2×C33 | C3⋊Dic3 |
| LCS | G ▷ 3−1+2⋊C9 | |
| UCS | C1 ◁ C4 | |
149 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 149 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
2^3,3^5|a^2=b,b^2=c,d^3=g,e^3=g,d^a=d^2g^2,e^a=e^2g^2,f^a=fh^2,g^a=g^2,h^a=h^2,e^d=ef,f^e=fh120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 66);