Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C83 ⋊ #1708 |
190 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=d,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^c=h^82940 conjugacy classes — view the full character table.
| maximal subgroup of | #35292278, #35292280, #35318168, … |
| maximal normal subgroup of | #35292278, #35292280, #35318168, … |
| maximal quotient of | #35298176, #35304137, #35304145, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4109);