Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #559×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2198 |
246 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|b^2=g,c^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^82,e^b=efg,d^c=df,e^d=eg1045 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35325123, #35325124, #35325128, … |
| maximal normal subgroup of | #35325123, #35325124, #35325128, … |
| maximal quotient of | #35316444, #35316472, #35316615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6506);