Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C9 ⋊ C8×C4⋊C4 |
444 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1152 |
Polycyclic presentation:
2^7,3^2|a^2=e,b^2=f,c^2=de,e^2=g,h^3=i,b^a=bd,h^a=h^2i^2,i^a=i^2,h^b=h^2i^2,i^b=i^2,h^c=h^2i^2,i^c=i^2240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 18264);