Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C32×M16 ⋊ D4 |
| Sylow | C32 ⋊ #3055 |
846 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 111 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|b^2=e,e^2=g,b^a=be,c^a=cf,e^a=eg,i^a=hi^2,d^b=dg,h^c=hi,i^c=i^2,h^f=h^2,i^f=i^263 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/8)×GO+(4,𝔽2) |
| maximal normal subgroup of | AGL(1,ℤ/8)×GO+(4,𝔽2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 101212);