Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#2258⋊C3) |
| unambiguous semidirect product | #71451⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D3×A4 |
| commutator, hypocenter | C3×Q8 | C3×C16 |
| Fitting, cosocle | C3×#504 | C2×C3 |
| socle | C2×C3 | A4×C16 |
| prime radical | C3×#41⋊C3 | C8 |
| LCS | G ▷ C3×Q8 | |
| UCS | C1 ◁ C16 | |
81 conjugacy classes of subgroups.
| minimal degree | μ(G) = 131 |
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2,3,2^5,3,2|a^2=c,c^2=d,d^2=e,e^2=i,f^2=i,g^2=i,h^a=h^2,f^b=fg,g^b=f,g^f=gi168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154177);