Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C2×C33 |
No aliases for this group.
| Fitting | C22×C32⋊C9 ⋊ C3 |
| Sylow | C22 ⋊ C9⋊H(3,𝔽3) |
189 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 189 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
3^5,2^2|b^3=d,c^a=cde,f^a=fg,g^a=f,c^b=ce84 conjugacy classes — view the full character table.
| maximal subgroup of | #11757779⋊C2, C2×#11757779 |
| maximal normal subgroup of | #11757779⋊C2, C2×#11757779 |
| maximal quotient of | #14517176, C2×#11757779 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 504);