Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Fitting | C32×#413 ⋊ C2 |
| Sylow | C32 ⋊ #1796 |
1608 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 1608 conjugacy classes of subgroups — too many to draw. Only its 221 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,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,i^a=i^2,d^b=dg,h^b=h^2,i^b=i^2,f^c=fg117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 19011);