Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
689 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 689 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^4,3^2,2^3|a^2=d,b^2=d,g^2=i,h^2=i,c^a=ci,f^a=f^2,c^b=ci,e^b=e^2,g^b=gh,h^b=hi,g^e=h,h^e=ghi,h^g=hi72 conjugacy classes — view the full character table.
| maximal subgroup of | #72226130, #72258803 |
| maximal normal subgroup of | #72258803 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 156183);