Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C32×Q8 ⋊ SD16 |
| Sylow | C32 ⋊ #3392 |
486 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 102 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=g,b^2=e,c^2=e,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2i,i^a=hi,d^b=de,f^c=fg,h^c=hi,i^c=i^2,h^f=h^2i^2,i^f=h^2i,h^g=h^2,i^g=i^245 conjugacy classes — view the full character table.
| maximal subgroup of | #41×AΓL(1,𝔽9), #72220224, #72220444, … |
| maximal normal subgroup of | #41×AΓL(1,𝔽9), #72220224, #72220444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 132343);