Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #1839 |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=hi,i^a=hi^2,h^f=h^2,i^f=i^2120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 20139);