Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C32×AGL(1,ℤ/8) ⋊ C22 |
| Sylow | C32 ⋊ C2×#453 |
1837 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,f^b=fg,e^c=eg,i^c=hi^2,h^d=h^2,i^d=i^275 conjugacy classes — view the full character table.
| maximal subgroup of | #72220386, D32×#453, #72257988, … |
| maximal normal subgroup of | D32×#453, #72257988, #72257996, … |
| maximal quotient of | #72220386, C2×#11864773 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 98784);