Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C32 ⋊ #3360 |
745 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^7,3^2|b^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,i^a=hi^2,d^b=de,f^c=fg,h^c=h^2,i^c=h^2i,h^d=h^2,i^d=h^2i96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 129296);