Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C32×SD16 ⋊ D4 |
| Sylow | C32 ⋊ #3265 |
844 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,i^a=hi^2,d^b=de,e^b=eg,h^c=hi,i^c=i^2,e^d=eg,h^f=h^2,i^f=i^254 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/8)×GO+(4,𝔽2) |
| maximal normal subgroup of | AGL(1,ℤ/8)×GO+(4,𝔽2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 118051);