Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C9×#470 ⋊ C2 |
| Sylow | C9 ⋊ #3204 |
603 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 603 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=g,b^2=g,d^2=g,f^2=g,h^3=i,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,f^c=fg,h^c=h^2i^2,i^c=i^2,h^d=h^2i^2,i^d=i^290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 112558);