Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#1747⋊C3) |
| unambiguous semidirect product | #68717⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D3×C42⋊C3 |
| commutator, Fitting, cosocle, hypocenter | C3×#338 | C2×C3 |
| Frattini | C22×C4 | D3×A4 |
| socle | C2×C3 | #376⋊C3 |
| prime radical | C3×#338⋊C3 | C2 |
| LCS | G ▷ C3×#338 | |
| UCS | C1 ◁ C4 | |
107 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2,3,2^2,3,2^4|a^2=fh,c^2=f,d^2=fg,f^2=i,e^a=e^2,c^b=d,d^b=cdg,f^b=fg,g^b=hi,h^b=gh,d^c=dfh,g^c=gi,f^d=fi,g^d=gi,h^d=hi54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154160);