Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #2258⋊C9 |
| Sylow | #2258 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C32 | A4 |
| commutator, hypocenter | Q8 | C9×C16 |
| Frattini | C3×C16 | C2×A4 |
| Fitting | C3×#2258 | C3 |
| socle | C2×C3 | A4×C16 |
| prime radical | C3×#41 | C3×C8 |
| cosocle | C3×#504 | C2×C3 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C3×C32 | |
61 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2,3,2,3,2^5|a^2=c,b^3=d,c^2=e,e^2=f,f^2=i,g^2=i,h^2=i,g^b=h,h^b=ghi,h^g=hi336 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153396);