Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #1843⋊C9 |
| Sylow | #1843 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | #127⋊C3 |
| commutator, hypocenter | #95 | C4×C9 |
| Frattini | C22×C3×C4 | C2×A4 |
| Fitting | C3×#1843 | C3 |
| socle, prime radical | C23×C3 | C4×A4 |
| cosocle | C3×#376 | C2×C3 |
| LCS | G ▷ #95 | |
| UCS | C1 ◁ C3×C4 | |
111 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2,3,2,3,2^5|a^2=c,b^3=d,c^2=i,e^2=g,f^2=h,b^a=bhi,e^a=egi,f^a=fhi,e^b=fgi,f^b=efi,g^b=h,h^b=ghi,f^e=fi108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153370);