Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of C3⋊#4185 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C33 |
| unambiguous semidirect product | C3⋊#66332 |
| derived, Sylow | C3×#732 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊#4185 |
| commutator, hypocenter | C3×#732 | C4 |
| Frattini | C2×C32 | C3⋊(C3⋊D3) |
| Fitting, prime radical, cosocle | C2×C3×#732 | C2 |
| socle | C2×C32 | #272 |
| LCS | G ▷ C3×#732 | |
| UCS | C1 ◁ C2 | |
228 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2^2,3^5|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2,g^a=g^2,e^d=ef,f^d=fg,f^e=fg^260 conjugacy classes — view the full character table.
| maximal subgroup of | #14517053, #14517054, #4179⋊Dic3, … |
| maximal normal subgroup of | #14517053, #14517054, #4179⋊Dic3, … |
| maximal quotient of | C3⋊#10619511, C2×C3⋊#66332 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 371);