Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of C3⋊#4169 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C3⋊#66316 |
| derived | C32×C9 ⋊ C3×C4 |
| Sylow | C3×C32⋊C9 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊#4169 |
| commutator, hypocenter | C32×C9 | C3×C4 |
| Frattini | C2×C32 | C3×C3⋊D3 |
| Fitting | C2×C3×C32⋊C9 | C2 |
| socle | C2×C33 | C3×D3 |
| prime radical | C2×C34 | D3 |
| cosocle | C2×C32×C9 | C2×C3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C2 | |
284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 86 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:
2,3,2,3^4|a^2=c,d^3=g,d^a=d^2g^2,e^a=e^2,f^a=f^2,g^a=g^2,d^b=df108 conjugacy classes — view the full character table.
| maximal subgroup of | #14516762, Dic3×#4169, D3×#66316, … |
| maximal normal subgroup of | #14516762, Dic3×#4169, D3×#66316, … |
| maximal quotient of | C3⋊#10619495, C2×C3⋊#66316 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 321);