Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C32×M16 ⋊ D4 |
| Sylow | C32 ⋊ #2006 |
640 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=hi^2,c^b=cf,d^b=dg,i^b=hi^2,e^c=eg,h^c=hi,i^c=i^2,h^e=h^2,i^e=i^2,h^f=h^2,i^f=i^251 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 26269);