Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C9×#343 ⋊ C2 |
| Sylow | C9 ⋊ C4×#100 |
540 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 136 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=e,b^2=f,c^2=e,f^2=g,h^3=i,b^a=bd,f^a=fg,d^b=dg,h^c=h^2i^2,i^c=i^2132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17780);