Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Fitting | C22×C3×C22⋊C4 ⋊ D3 |
1102 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^2,2^2|c^2=d,b^a=be,f^a=f^2,g^a=g^2,h^a=hi,c^b=ce,h^f=i,i^f=hi90 conjugacy classes — view the full character table.
| maximal subgroup of | #72241520, D3×GL(2,ℤ/4)⋊C4, #72252920, … |
| maximal normal subgroup of | D3×GL(2,ℤ/4)⋊C4, #72252920, #72252962 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 156857);