Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C3)⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C33 |
| unambiguous semidirect product | ((C3⋊D3)⋊C3)⋊(C3⋊Dic3) |
| derived, Sylow | C32×H(3,𝔽3) ⋊ C2×C4 |
1180 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 1180 conjugacy classes of subgroups — too many to draw. Only its 212 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,g^a=g^2,h^a=h^2,d^b=d^2,e^b=e^2,f^b=f^2,h^b=h^2,g^f=gh102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3168);