Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #87207⋊C3 |
| Fitting | C3×#577 ⋊ C2×C3 |
696 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 77 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,e^2=i,f^2=i,g^2=i,c^a=ci,h^a=h^2,c^b=ce,e^b=ei,e^c=ei,f^d=fg,g^d=f,g^f=gi69 conjugacy classes — view the full character table.
| maximal subgroup of | #72242413, D3×#3585⋊C3, #72242438, … |
| maximal normal subgroup of | D3×#3585⋊C3, #72242438, #72242445 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157346);