Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C83 ⋊ #2241 |
140 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=e,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,h^a=h^822662 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35318026, #35318027, #35318033, … |
| maximal normal subgroup of | #35318026, #35318027, #35318033, … |
| maximal quotient of | #35320784, #35322327, #35322622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6738);