Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #3573 |
2234 conjugacy classes of subgroups; only the 750 normal subgroups are shown.
This group has 2234 conjugacy classes of subgroups — too many to draw. Only its 750 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=f,f^2=g,h^a=hi,i^a=hi^2,e^b=eg,d^c=dg,h^c=h^2,i^c=i^2,h^d=h^2,i^d=i^2,h^f=h^2,i^f=i^2102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152529);