Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C28 |
| unambiguous semidirect product | C22⋊(C22⋊(Q8⋊C9)) |
| derived, Sylow | C24×Q8 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C22⋊(C22⋊A4) |
| commutator, hypocenter | C24×Q8 | C9 |
| Fitting, cosocle | C24×C3×Q8 | C3 |
| socle, prime radical | C25×C3 | A4 |
| LCS | G ▷ C24×Q8 | |
| UCS | C1 ◁ C2×C3 | |
2207 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
3^2,2^7|a^3=b,c^2=i,d^2=i,c^a=cd,d^a=c,e^a=f,f^a=ef,g^a=egh,h^a=fg,d^c=di96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153920);