Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C128 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C32 ⋊ C128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | AGL(1,𝔽9) |
| commutator, hypocenter | C32 | C128 |
| Fitting | C32×C16 | C8 |
| socle, prime radical | C2×C32 | C64 |
| cosocle | #10589065 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C16 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^7,3^2|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^2i,i^a=h,h^b=h^2i^2,i^b=h^2i,h^c=h^2,i^c=i^2144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 4661);