Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C28 |
No aliases for this group.
| derived, Sylow | 2−1+6 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C2×C3 | C22⋊(C22⋊A4) |
| commutator, hypocenter | 2−1+6 | C9 |
| Fitting, prime radical, cosocle | C3×2−1+6 | C3 |
| LCS | G ▷ 2−1+6 | |
| UCS | C1 ◁ C2×C3 | |
2058 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
3^2,2^7|a^3=b,e^2=i,f^2=i,c^a=d,d^a=cd,e^a=ef,f^a=e,g^a=h,h^a=gh,h^c=hi,g^d=gi,f^e=fi81 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153924);