Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Fitting | C32×C42 ⋊ C8 |
| Sylow | C32 ⋊ #1744 |
350 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,h^a=h^2i,i^a=h,h^e=h^2i^2,i^e=h^2i,h^g=h^2,i^g=i^296 conjugacy classes — view the full character table.
| maximal subgroup of | #72252932, #72252950, #97×AGL(1,𝔽9) |
| maximal normal subgroup of | #72252932, #72252950, #97×AGL(1,𝔽9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17494);