Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C9×#127 ⋊ C2 |
| Sylow | C9 ⋊ #2011 |
765 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 765 conjugacy classes of subgroups — too many to draw. Only its 140 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|d^2=g,e^2=g,h^3=i,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2i^2,i^a=i^2,c^b=cf,d^b=dg,e^b=eg,d^c=dg,e^c=eg144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 26443);