Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C22 ⋊ #6875 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
3^5,2^2|a^3=d,b^3=c,c^3=e,d^3=e,b^a=bd,c^a=ce,f^a=fg,g^a=f,d^b=de^268 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11757430, A4×#6875, #72229244, … |
| maximal normal subgroup of | C2×#11757430, A4×#6875 |
| maximal quotient of | #14515865, C2×#11757430, #72229244, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 155);