Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×C9×#41 ⋊ C2 |
| Sylow | C9 ⋊ #3475 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D9 |
| commutator, cosocle | C22×C9 | C25 |
| Frattini, socle | C22×C3 | C24×D3 |
| Fitting | C4×C9×#41 | C2 |
| hypercenter | C4×#41 | D9 |
| hypocenter | C9 | #3475 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C2×C4 ◁ C4×#41 | |
1698 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|b^2=g,e^2=f,h^3=i,b^a=bf,c^a=cg,h^a=h^2i^2,i^a=i^2,d^b=df,h^d=h^2i^2,i^d=i^2210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 137475);