Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C32×#451 ⋊ C2 |
| Sylow | C32 ⋊ #1606 |
780 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 117 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=f,c^2=fg,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=eg,h^b=h^2,i^b=i^2,d^c=dg,h^c=h^2,i^c=i^299 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 12398);