Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C32×#41 ⋊ D4 |
| Sylow | C32 ⋊ #3018 |
1260 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,i^a=hi^2,e^b=eg,f^b=fg,e^c=eg,h^c=hi,i^c=i^2,h^f=h^2,i^f=i^266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99021);