Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1710 |
168 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=dg,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^822662 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291126, #35318715, #35318716, … |
| maximal normal subgroup of | #35291126, #35318715, #35318716, … |
| maximal quotient of | #35298181, #35304149, #35304163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4120);