Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #2230 |
126 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 49 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=df,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=ef,f^a=fg,h^a=h^82,e^c=efg,f^c=fg1171 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35318163, #35318165, #35318168, … |
| maximal normal subgroup of | #35318163, #35318165, #35318168, … |
| maximal quotient of | #35320505, #35321101, #35322103, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6681);