Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
408 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 47 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:
2^5,3^2,2^2|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,g^a=g^2,c^b=ce,f^b=f^2,h^b=hi,h^f=i,i^f=hi66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154656);