Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D3×((C3⋊D3)⋊C3)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (((C3⋊D3)⋊C3)⋊D3)⋊C4 |
| derived, Sylow | C3×H(3,𝔽3) ⋊ C22×C4 |
524 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 69 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:
2^4,3^4|b^2=d,c^2=d,g^a=g^2,h^a=h^2,e^b=e^2,h^b=h^2,f^c=f^2,g^e=gh66 conjugacy classes — view the full character table.
| maximal subgroup of | #72219732, #72222983, #72259582, … |
| maximal normal subgroup of | #72219732 |
| maximal quotient of | #72213798, #72222983, #72259582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2044);