Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C4×C8×C9 ⋊ C2 |
| Sylow | C9 ⋊ #1753 |
522 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=e,b^2=f,c^2=e,e^2=g,h^3=i,b^a=bd,c^a=cg,h^a=h^2i^2,i^a=i^2312 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17713);