Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C3×C4 |
No aliases for this group.
| Fitting | C32×C42 ⋊ Q8 |
| Sylow | C32 ⋊ #2868 |
702 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 195 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|a^2=e,b^2=e,c^2=f,d^2=g,b^a=be,c^a=cf,d^a=dg,h^a=hi,i^a=hi^2,h^b=i,i^b=h^2,h^d=i^2,i^d=h,h^e=h^2,i^e=i^2,h^g=h^2,i^g=i^260 conjugacy classes — view the full character table.
| maximal subgroup of | #127×PSU(3,𝔽2), #72220536, #72220538, … |
| maximal normal subgroup of | #127×PSU(3,𝔽2), #72220536, #72220538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 91104);