Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ #1520 |
354 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 60 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,c^2=g,d^2=g,b^a=bd,c^a=cg,d^a=df,h^a=hi,i^a=i^2,c^b=cf,d^b=dg,e^b=efg,h^b=i,i^b=h^2,h^c=hi,i^c=hi^2,h^d=h^2i^2,i^d=h^2i,h^f=h^2,i^f=i^2,h^g=h^2,i^g=i^242 conjugacy classes — view the full character table.
| maximal subgroup of | #72220469, #72252879, #72252885, … |
| maximal normal subgroup of | #72220469, #72252879, #72252885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 9630);