Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C32×C4×C8 ⋊ C22 |
| Sylow | C32 ⋊ #2972 |
1059 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=f,f^2=g,b^a=be,d^a=de,i^a=hi^2,c^b=ce,i^b=hi^2,i^c=hi^2,h^d=h^2,i^d=i^2180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 96183);