Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C9×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C9 ⋊ #3585 |
2196 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|f^2=g,h^3=i,b^a=bf,e^a=eg,f^a=fg,f^b=fg,d^c=dg,h^d=h^2i^2,i^d=i^2129 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#3585, #72268975, #72268983, … |
| maximal normal subgroup of | D9×#3585, #72268975, #72268983, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153031);