Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #510×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3417 |
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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=g,b^2=g,e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,e^b=ef,f^b=fg,h^b=h^82,d^c=dg,h^d=h^82688 conjugacy classes — view the full character table.
| maximal subgroup of | #35561158, #35561160, #35561169, … |
| maximal normal subgroup of | #35561158, #35561160, #35561169, … |
| maximal quotient of | #35557321, #35557322, #35557447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17662);