Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊#10619756 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | C3⋊#10619756 |
| derived | C3×#66361 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×#66361 | C2 |
| Frattini | C32 | C3⋊(C3⋊S4) |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | #272 |
| LCS | G ▷ C3×#66361 | |
| UCS | C1 | |
345 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 345 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) = 162 |
Polycyclic presentation:
2,3^5,2^2|b^3=f^2,b^a=b^2f,c^a=c^2,d^a=d^2,f^a=f^2,g^a=gh,d^b=de,e^b=ef,g^b=h,h^b=gh,e^d=ef^251 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2511);