Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C9×C4⋊C8 ⋊ C2 |
| Sylow | C9 ⋊ #2906 |
726 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=e,f^2=g,h^3=i,b^a=be,d^c=dg,h^d=h^2i^2,i^d=i^2210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 92340);