Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Fitting | C32×#476 ⋊ C2 |
| Sylow | C32 ⋊ #3118 |
1218 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,i^a=i^2,d^b=dg,h^b=h^2,i^b=i^2,f^c=fg,h^d=h^2,i^d=i^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 106127);