Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #361×C83 ⋊ C2 |
| Sylow | C83 ⋊ AGL(1,ℤ/16) |
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=e,c^2=efg,d^2=f,f^2=g,b^a=bd,c^a=cf,d^a=df,f^a=fg,h^a=h^82,d^b=dfg,e^b=eg,f^b=fg,h^b=h^82,d^c=dg,h^c=h^82679 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/16)×D83, C2×#24909364, #35557851, … |
| maximal normal subgroup of | AGL(1,ℤ/16)×D83, C2×#24909364, #35557851, … |
| maximal quotient of | #35316274, #35316286, #35316352, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6411);