Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C22×C32⋊C9 ⋊ C3 |
| Sylow | C22 ⋊ #6859 |
95 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
3^5,2^2|b^3=d^2,b^a=bc,c^a=cd,f^a=fg,g^a=f,c^b=ce68 conjugacy classes — view the full character table.
| derived subgroup of | #14516470 |
| maximal subgroup of | #14516426, #14516470, #14516512, … |
| maximal normal subgroup of | #14516426, #14516470, #14516512, … |
| maximal quotient of | #14515844, C2×#11757411 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 136);