Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C9 ⋊ #1316 |
441 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 441 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|a^2=d,d^2=f,h^3=i,b^a=bc,c^a=ce,e^a=eg,h^a=h^2i^2,i^a=i^2,d^b=de,d^c=dg138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 5374);