Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C32×C4⋊C8 ⋊ C4 |
| Sylow | C32 ⋊ #1296 |
326 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=d,b^2=e,c^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=hi,i^a=hi^2,c^b=cg,h^d=h^2,i^d=i^278 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 5093);