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×#41 ⋊ C4 |
| Sylow | C32 ⋊ #3428 |
2430 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|a^2=g,e^2=f,b^a=bf,d^a=df,h^a=hi,i^a=hi^2,c^b=cf,h^g=h^2,i^g=i^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134137);