Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C9 ⋊ #1705 |
321 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 321 conjugacy classes of subgroups — too many to draw. Only its 98 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|b^2=d,c^2=e,d^2=f,e^2=g,h^3=i,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^c=h^2i^2,i^c=i^2126 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#1705, #72244462, #72244491, … |
| maximal normal subgroup of | D9×#1705, #72244462, #72244491, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 16425);