Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C2×C33 |
No aliases for this group.
| Fitting | C22×C3×3−1+2 ⋊ C3 |
| Sylow | C22 ⋊ #6910 |
174 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=ce,d^c=de68 conjugacy classes — view the full character table.
| maximal subgroup of | (#66365⋊C2)⋊C3, C2×#11757850, #72228403, … |
| maximal normal subgroup of | (#66365⋊C2)⋊C3, C2×#11757850, #72228403, … |
| maximal quotient of | #14517256, C2×#11757850 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 575);