Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C2×C34 |
No aliases for this group.
| Fitting | C22×C3×3−1+2 ⋊ C3 |
| Sylow | C22 ⋊ #6911 |
198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
3^5,2^2|c^3=e,c^a=cd,d^a=de^2,f^a=fg,g^a=f,c^b=ce68 conjugacy classes — view the full character table.
| maximal subgroup of | #14517986, #14518076, #14518203, … |
| maximal normal subgroup of | #14517986, #14518076, #14518203, … |
| maximal quotient of | #14517258, C2×#11757852 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 577);