Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C3×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #1771 |
310 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=e,b^2=f,c^2=de,e^2=g,b^a=bd,c^a=cg,h^a=hi,i^a=hi^2,h^b=i^2,i^b=h,h^d=h^2,i^d=i^2,h^e=h^2,i^e=i^2,h^f=h^2,i^f=i^272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 18368);