Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ #1390 |
432 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 39 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=d,b^2=e,b^a=bc,c^a=cf,f^a=fg,i^a=hi^2,d^b=df,h^b=hi,i^b=hi^2,d^c=dg,h^c=h^2,i^c=i^2,h^e=h^2,i^e=i^248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 6574);