Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C32×C4⋊C4 ⋊ C8 |
| Sylow | C32 ⋊ #1279 |
254 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 69 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=d,b^2=e,c^2=f,d^2=g,e^2=fg,b^a=bc,c^a=cf,e^a=ef,h^a=i,i^a=hi,h^b=h^2i,i^b=h,h^d=hi,i^d=hi^2,h^e=h^2i^2,i^e=h^2i,h^g=h^2,i^g=i^266 conjugacy classes — view the full character table.
| maximal subgroup of | #72269009, #72269025, #106×AGL(1,𝔽9) |
| maximal normal subgroup of | #72269009, #72269025, #106×AGL(1,𝔽9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 4807);