Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C2×C32 |
No aliases for this group.
| Sylow | C22 ⋊ #6867 |
122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
3^5,2^2|a^3=c,b^3=e,b^a=bd,d^a=de,f^a=fg,g^a=f132 conjugacy classes — view the full character table.
| derived subgroup of | #14516485 |
| maximal subgroup of | #14516443, #14516485, #14516530, … |
| maximal normal subgroup of | #14516443, #14516485, #14516530, … |
| maximal quotient of | #14515879, C2×#11757446 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 171);