Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #1651 |
268 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 42 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=fg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=hi,i^a=i^2,d^b=df,e^b=eg,h^b=i,i^b=h^2,d^c=dg,e^c=eg,h^d=h^2i^2,i^d=h^2i,h^f=h^2,i^f=i^233 conjugacy classes — view the full character table.
| maximal subgroup of | #72220125, SD16×AΓL(1,𝔽9), #72220191, … |
| maximal normal subgroup of | SD16×AΓL(1,𝔽9), #72220191, #72220197, … |
| maximal quotient of | #72252880, #72269009 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 14326);