Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | C32⋊C9 ⋊ C3×C4 |
| Sylow | #6859 ⋊ C4 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2,3,2,3^4|a^2=c,d^3=f,d^a=d^2f^2,e^a=e^2g,f^a=f^2,d^b=de,e^b=ef^2,e^d=eg62 conjugacy classes — view the full character table.
| maximal subgroup of | #92201⋊C4, #92164⋊C4, #14515740, … |
| maximal normal subgroup of | #92201⋊C4, #92164⋊C4, #14515740, … |
| maximal quotient of | #14515623, C2×#11757286 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 11);