Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Fitting | C32×D8 ⋊ Q8 |
| Sylow | C32 ⋊ #3384 |
412 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^7,3^2|a^2=e,b^2=e,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=i,i^a=h^2,c^b=cg,d^b=de,h^b=hi,i^b=hi^2,f^c=fg,h^d=i^2,i^d=h,h^e=h^2,i^e=i^236 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/8)×PSU(3,𝔽2), #72220229, #72220233 |
| maximal normal subgroup of | AGL(1,ℤ/8)×PSU(3,𝔽2), #72220229, #72220233 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 131614);