Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | 3−1+4 ⋊ C4 |
322 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2,3^2,2,3^3|a^2=d,c^3=g,e^a=e^2,f^a=f^2,c^b=cg,f^e=fg116 conjugacy classes — view the full character table.
| maximal subgroup of | #10619833⋊C3, #10619905⋊C3, (#4207⋊C3)⋊C4, … |
| maximal normal subgroup of | #10619833⋊C3, #10619905⋊C3, (#4207⋊C3)⋊C4, … |
| maximal quotient of | #14517878, C2×#11758015, #72247508 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 740);