Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #87277⋊C3 |
| Fitting | C2×C3×H(5,𝔽2) ⋊ C2×C3 |
713 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 713 conjugacy classes of subgroups — too many to draw. Only its 83 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:
2^3,3,2^3,3,2|b^2=i,c^2=i,e^2=i,f^2=i,g^2=i,c^a=ce,e^a=ei,h^a=h^2,c^b=ci,e^c=ei,f^d=fg,g^d=f,g^f=gi81 conjugacy classes — view the full character table.
| maximal subgroup of | #72242417, D3×#3585⋊C3, #72242450, … |
| maximal normal subgroup of | D3×#3585⋊C3, #72242450, #72252926 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157402);