Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C3 |
No aliases for this group.
| Fitting | C2×C32×#131 ⋊ C2 |
| Sylow | C32 ⋊ #3573 |
4272 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|a^2=f,f^2=g,e^b=eg,d^c=dg,h^e=h^2,i^e=i^2228 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152520);