Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #1915 |
308 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 93 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=f,b^2=dfg,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^82,d^b=dg,e^b=eg,f^b=fg,h^b=h^82,d^c=dg,f^c=fg931 conjugacy classes — view the full character table.
| maximal subgroup of | #35320188, #35320191, #35320195, … |
| maximal normal subgroup of | #35320188, #35320191, #35320195, … |
| maximal quotient of | #35299945, #35299955, #35300398, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5063);