Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #84128⋊C3 |
| Fitting | C26×C3 ⋊ C2×C3 |
1289 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 1289 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^2,3,2^5,3|b^a=bd,e^a=eg,f^a=fgh,i^a=i^2,e^c=ef,f^c=e,g^c=h,h^c=gh60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AΣL(1,𝔽64), #72228419, #72229182, … |
| maximal normal subgroup of | D3×AΣL(1,𝔽64), #72228419, #72229182, … |
| maximal quotient of | C2×#84128⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155397);