Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C32 ⋊ C2×AΣL(1,𝔽16) |
862 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 862 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^7,3^2|a^2=e,b^a=bd,d^a=df,f^a=fg,h^a=hi,i^a=hi^2,e^b=ef,i^b=hi^2,h^c=h^2,i^c=i^2,e^d=eg,h^d=h^2,i^d=i^2,h^e=h^2,i^e=i^251 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 30167);