Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C32×C4×C16 ⋊ C2 |
| Sylow | C32 ⋊ D4⋊C16 |
330 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=d,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^2,i^a=i^2,c^b=ce,h^b=h^2,i^b=i^2312 conjugacy classes — view the full character table.
| maximal subgroup of | #72269802 |
| maximal normal subgroup of | #72269802 |
| maximal quotient of | #72269806 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 5543);