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 ⋊ #6866 |
392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
3^5,2^2|a^3=c,b^a=bd,d^a=de,f^a=fg,g^a=f132 conjugacy classes — view the full character table.
| derived subgroup of | #14516501 |
| maximal subgroup of | #14516453, #14516501, #14516540, … |
| maximal normal subgroup of | #14516453, #14516501, #14516540, … |
| maximal quotient of | #14515896, C2×#11757461 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 186);