Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C32×D4 ⋊ D4 |
| Sylow | C32 ⋊ #3036 |
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,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,i^a=hi^2,h^b=hi,i^b=hi^2,f^c=fg,h^e=h^2,i^e=i^254 conjugacy classes — view the full character table.
| maximal subgroup of | #72220197, AGL(1,ℤ/8)×GO+(4,𝔽2), #72220238 |
| maximal normal subgroup of | #72220197, AGL(1,ℤ/8)×GO+(4,𝔽2), #72220238 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99908);