Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×#131×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3584 |
1424 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|e^2=g,f^2=g,b^a=bf,f^a=fg,h^a=h^82,f^b=fg,h^b=h^82,d^c=dg1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35320109, #35320112, #35320114, … |
| maximal normal subgroup of | #35320109, #35320112, #35320114, … |
| maximal quotient of | #36267970, #36268083, #36268525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19284);