Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C22×C3×C27 ⋊ C3 |
| Sylow | C22 ⋊ #6872 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
3^5,2^2|b^3=c,c^3=e,b^a=bd,d^a=de^2,f^a=fg,g^a=f132 conjugacy classes — view the full character table.
| derived subgroup of | #14516478 |
| maximal subgroup of | #14516438, #14516478, #14516522, … |
| maximal normal subgroup of | #14516438, #14516478, #14516522, … |
| maximal quotient of | #14515863, C2×#11757428 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 153);