Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C32×C42 ⋊ C8 |
| Sylow | C32 ⋊ #1842 |
354 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=d,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^2i,i^a=h,h^f=h^2i^2,i^f=h^2i,h^g=h^2,i^g=i^272 conjugacy classes — view the full character table.
| maximal subgroup of | #72220422, #127×AGL(1,𝔽9), #72220536 |
| maximal normal subgroup of | #72220422, #127×AGL(1,𝔽9), #72220536 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 20196);