Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | #2811 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, prime radical, hypercenter | C23×C3 | C22⋊A4 |
| commutator, hypocenter | #2811 | C9 |
| Fitting, cosocle | C3×#2811 | C3 |
| LCS | G ▷ #2811 | |
| UCS | C1 ◁ C23×C3 | |
242 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1152 |
Polycyclic presentation:
3^2,2^7|a^3=b,c^2=g,d^2=ghi,e^2=ghi,f^2=g,c^a=f,d^a=de,e^a=d,f^a=cfg,d^c=dgh,e^c=egh,f^c=fg,e^d=eghi,f^d=fgh96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153664);