Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C9×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C9 ⋊ #3068 |
699 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|b^2=e,e^2=g,f^2=g,h^3=i,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=dg,f^c=fg,h^c=h^2i^2,i^c=i^2117 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#3068, #72268953, #72269008 |
| maximal normal subgroup of | D9×#3068, #72268953, #72269008 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 102084);