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 ⋊ #6909 |
186 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
3^5,2^2|c^3=e,c^a=cd,d^a=de,f^a=fg,g^a=f,c^b=ce,d^c=de68 conjugacy classes — view the full character table.
| maximal subgroup of | (#66366⋊C2)⋊C3, C2×#11757851, A4×#6909, … |
| maximal normal subgroup of | (#66366⋊C2)⋊C3, C2×#11757851, A4×#6909, … |
| maximal quotient of | #14517257, C2×#11757851 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 576);