Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C32 ⋊ #2004 |
690 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 55 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|b^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fg,c^b=cf,d^b=dg,i^b=hi^2,d^c=dg,h^c=hi,i^c=i^2,h^f=h^2,i^f=i^254 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 26181);