Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C2×C32 |
No aliases for this group.
| Sylow | C22 ⋊ #6868 |
122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
3^5,2^2|a^3=d,b^3=e^2,b^a=bc,c^a=ce,f^a=fg,g^a=f132 conjugacy classes — view the full character table.
| derived subgroup of | #14516486 |
| maximal subgroup of | #14516442, #14516486, #14516529, … |
| maximal normal subgroup of | #14516442, #14516486, #14516529, … |
| maximal quotient of | #14515880, C2×#11757447 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 172);