Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C9×#356 ⋊ C2 |
| Sylow | C9 ⋊ #2132 |
375 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 375 conjugacy classes of subgroups — too many to draw. Only its 68 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=e,c^2=g,d^2=g,e^2=g,h^3=i,b^a=bd,d^a=df,f^a=fg,d^b=dg,e^b=efg,h^b=h^2i^2,i^b=i^2,h^c=h^2i^2,i^c=i^2,e^d=eg78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 30504);