Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C2×C32 |
No aliases for this group.
| Fitting | C22×C3×C27 ⋊ C3 |
| Sylow | C22 ⋊ #6903 |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
3^5,2^2|c^3=d,d^3=e,b^a=be,f^a=fg,g^a=f180 conjugacy classes — view the full character table.
| maximal subgroup of | #14518021, #14518023, #14518235, … |
| maximal normal subgroup of | #14518021, #14518023, #14518235, … |
| maximal quotient of | #14517202, C2×#11757795 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 520);