Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
422 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 95 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=d,b^2=c,c^2=e,b^a=be,f^a=f^2,g^a=g^2,h^a=hi,h^f=i,i^f=hi120 conjugacy classes — view the full character table.
| maximal subgroup of | #72253047, #97×C3⋊S4 |
| maximal normal subgroup of | #97×C3⋊S4 |
| maximal quotient of | #72253047 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155075);