Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C9×#101 ⋊ C2 |
| Sylow | C9 ⋊ #1784 |
846 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=g,f^2=g,h^3=i,b^a=bd,c^a=ce,d^a=dg,f^b=fg,h^c=h^2i^2,i^c=i^2120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 18660);