Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| derived, Sylow | #2276 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C22⋊(C42⋊C3) |
| commutator, hypocenter | #2276 | C9 |
| Frattini, socle, prime radical | C23×C3 | C22⋊A4 |
| Fitting, cosocle | C3×#2276 | C3 |
| LCS | G ▷ #2276 | |
| UCS | C1 ◁ C2×C3 | |
249 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
3^2,2^7|a^3=b,c^2=h,d^2=g,e^2=gi,f^2=ghi,c^a=cd,d^a=cg,e^a=def,f^a=ceh,g^a=h,h^a=gh,i^a=hi,f^c=fghi,e^d=eghi84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153654);