Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3×C9 |
No aliases for this group.
| Fitting | C22×C92 ⋊ C3 |
| Sylow | C22 ⋊ #6879 |
71 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
3^5,2^2|b^3=d^2,c^3=e^2,b^a=bc,c^a=cde,d^a=de,f^a=fg,g^a=f116 conjugacy classes — view the full character table.
| derived subgroup of | #14516455 |
| maximal subgroup of | #14516418, #14516455, #14516507, … |
| maximal normal subgroup of | #14516418, #14516455, #14516507, … |
| maximal quotient of | #14515832, C2×#11757397 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 122);