Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C3×C4 |
No aliases for this group.
| Fitting | C32×C4×D4 ⋊ C4 |
| Sylow | C32 ⋊ #2275 |
1206 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=g,c^2=f,b^a=be,d^a=de,c^b=ce,h^b=hi,i^b=hi^2,h^g=h^2,i^g=i^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34922);