Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊#68006 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | C3⋊S4 |
| commutator, hypocenter | C3×SL(2,𝔽3) | C16 |
| Fitting | C3×#504 | D3 |
| socle | C2×C3 | A4⋊C16 |
| prime radical | C3×#41⋊C3 | C8 |
| cosocle | C3×#504⋊C3 | C2 |
| LCS | G ▷ C3×SL(2,𝔽3) | |
| UCS | C1 ◁ C16 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^4,3^2,2^3|a^2=b,b^2=c,c^2=d,d^2=i,g^2=i,h^2=i,e^a=e^2,f^a=f^2,g^a=gh,h^a=hi,g^e=h,h^e=ghi,h^g=hi120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154153);