Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C9×C4⋊C4 ⋊ C2 |
| Sylow | C9 ⋊ #2274 |
1044 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=g,c^2=e,h^3=i,b^a=be,d^a=de,c^b=ce,h^d=h^2i^2,i^d=i^2228 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34877);