Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C9 ⋊ #1414 |
126 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|a^2=d,b^2=f,c^2=f,e^2=g,h^3=i,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2i^2,i^a=i^2,c^b=cfg,d^b=defg,e^b=eg,h^b=h^2i^2,i^b=i^2,d^c=dfg,e^d=eg69 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 6908);