Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
166 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^5,3^2,2^2|a^2=e,b^2=e,c^2=de,d^2=e,f^3=g,b^a=bc,c^a=cd,d^a=de,f^a=f^2g^2,g^a=g^2,h^a=hi,c^b=cd,d^b=de,h^f=i,i^f=hi57 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154101);