Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C32×#131 ⋊ C22 |
| Sylow | C32 ⋊ #3573 |
2981 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=f,f^2=g,e^b=eg,h^b=h^2,i^b=i^2,d^c=dg,h^d=h^2,i^d=i^2,i^e=hi^2168 conjugacy classes — view the full character table.
| maximal subgroup of | #72222873 |
| maximal normal subgroup of | #72222873 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152533);