Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3×C4 |
No aliases for this group.
| Fitting | C2×C32×D8 ⋊ C4 |
| Sylow | C32 ⋊ #1972 |
714 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=dfg,c^2=e,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2i^2,i^a=h^2i,c^b=cg,h^b=hi,i^b=hi^2,h^f=h^2,i^f=i^260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 25111);