Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C22 ⋊ #6880 |
55 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
3^5,2^2|a^3=e,b^3=e,c^3=e,b^a=bc,c^a=cd,d^a=de^2,f^a=fg,g^a=f,c^b=cd,d^b=de^252 conjugacy classes — view the full character table.
| maximal subgroup of | #11757441⋊C2, C2×#11757441 |
| maximal normal subgroup of | #11757441⋊C2, C2×#11757441 |
| maximal quotient of | #14515876, C2×#11757441 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 166);