Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C9×#518 ⋊ C2 |
| Sylow | C9 ⋊ #3428 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D9 |
| commutator | C2×C9 | C24×C4 |
| Frattini, socle | C22×C3 | C24×D3 |
| Fitting | C9×#518 | C2 |
| prime radical | C22×#3699 | C2 |
| cosocle | C22×C9 | C25 |
| hypercenter | #518 | D9 |
| hypocenter | C9 | #3428 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ #518 | |
2310 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|a^2=g,e^2=f,h^3=i,b^a=bf,d^a=df,c^b=cf,h^e=h^2i^2,i^e=i^2204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134119);