Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C3)⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | ((C3⋊D3)⋊C3)⋊Dic3 |
| derived, Sylow | C3×H(3,𝔽3) ⋊ C2×C4 |
210 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 50 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:
2^3,3^4|b^2=c,f^a=f^2,g^a=g^2,d^b=d^2,e^b=e^2,g^b=g^2,f^d=fg42 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 401);