Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C3×C4 |
No aliases for this group.
| Fitting | C2×C32×M16 ⋊ C4 |
| Sylow | C32 ⋊ C2×H(3,ℤ/4) |
702 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|a^2=e,b^2=f,d^2=g,b^a=bd,f^a=fg,h^a=h^2i^2,i^a=h^2i,e^b=eg,h^b=hi,i^b=hi^2,h^c=h^2,i^c=i^2,h^e=h^2,i^e=i^2,h^f=h^2,i^f=i^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17147);