Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C32×Q16 ⋊ D4 |
| Sylow | C32 ⋊ #3288 |
727 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 727 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^2i^2,d^b=de,e^b=eg,i^b=hi^2,f^c=fg,h^c=h^2,i^c=i^2,e^d=eg,h^d=hi,i^d=i^2,h^e=h^2,i^e=i^251 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 120654);