Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C22×C9⋊C9 ⋊ C3 |
| Sylow | C22 ⋊ #6899 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×A4 |
| commutator, socle, cosocle | C22×C32 | C33 |
| Fitting | C22×C9⋊C9 | C3 |
| prime radical | C32×A4 | C32 |
| hypercenter | C9⋊C9 | A4 |
| hypocenter | C22 | #6899 |
| LCS | G ▷ C22×C32 ▷ C22 | |
| UCS | C1 ◁ C32 ◁ C9⋊C9 | |
127 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 127 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
3^5,2^2|b^3=d,c^3=e^2,b^a=be,c^a=cde,f^a=fg,g^a=f,c^b=ce84 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11757789 |
| maximal normal subgroup of | C2×#11757789 |
| maximal quotient of | #14517190, C2×#11757789 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 514);