Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C9×#95 ⋊ C2 |
| Sylow | C9 ⋊ #2275 |
1170 conjugacy classes of subgroups; only the 390 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 390 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=f,b^2=g,c^2=f,h^3=i,b^a=be,d^a=de,c^b=ce,h^d=h^2i^2,i^d=i^2228 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34907);