Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #4183⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #66330⋊C3 |
| derived | AΣL(1,𝔽27) ⋊ C3×C4 |
| Sylow | #6909 ⋊ C4 |
158 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2,3,2,3^4|a^2=c,d^a=d^2,e^a=e^2,f^a=fg^2,g^a=g^2,e^b=eg,e^d=ef,f^d=fg62 conjugacy classes — view the full character table.
| maximal subgroup of | #92281⋊C4, (#4175⋊C3)⋊C4, #10619550⋊C3, … |
| maximal normal subgroup of | #92281⋊C4, (#4175⋊C3)⋊C4, #10619550⋊C3, … |
| maximal quotient of | #10619509⋊C3, C2×#66330⋊C3, #72247271 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 360);