Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C32×C22⋊C4 ⋊ D4 |
| Sylow | C32 ⋊ #1898 |
1040 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 1040 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=df,b^a=bd,c^a=ce,d^a=dg,i^a=hi^2,d^b=dg,f^b=fg,h^c=hi,i^c=i^2,h^e=h^2,i^e=i^263 conjugacy classes — view the full character table.
| maximal subgroup of | #72241543, #99×GO+(4,𝔽2), #72253196 |
| maximal normal subgroup of | #72241543, #99×GO+(4,𝔽2), #72253196 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 22265);