Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #2227 |
130 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 55 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=dg,b^2=d,c^2=g,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^82,e^c=ef,f^c=fg,h^c=h^821669 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35318220, #35318221, #35318227, … |
| maximal normal subgroup of | #35318220, #35318221, #35318227, … |
| maximal quotient of | #35320451, #35321006, #35322076, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6663);