Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C83 ⋊ #1784 |
564 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 109 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=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,f^b=fg,h^b=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291756, #35291760, #35296539, … |
| maximal normal subgroup of | #35291756, #35291760, #35296539, … |
| maximal quotient of | #35295733, #35295747, #35295757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4433);