Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C2×C32×C4⋊C8 ⋊ C2 |
| Sylow | C32 ⋊ #1477 |
792 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=e,d^2=f,e^2=g,b^a=bd,d^a=df,c^b=cf,d^b=df,h^b=h^2,i^b=i^2204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 8274);