Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C32×D4 ⋊ C8 |
| Sylow | C32 ⋊ #2972 |
618 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 191 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=f,f^2=g,b^a=be,d^a=de,h^a=h^2i,i^a=h,c^b=ce,h^f=h^2i^2,i^f=h^2i,h^g=h^2,i^g=i^278 conjugacy classes — view the full character table.
| maximal subgroup of | #72220459, #72222908, H(5,𝔽2)×AGL(1,𝔽9), … |
| maximal normal subgroup of | #72220459, #72222908, H(5,𝔽2)×AGL(1,𝔽9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 96184);