Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C22×C32×C4 ⋊ D4 |
| Sylow | C32 ⋊ #3449 |
2446 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|e^2=f,b^a=bf,c^a=cg,d^a=df,i^a=hi^2,c^b=cf,h^c=hi,i^c=i^2,h^g=h^2,i^g=i^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 135259);