Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1713 |
192 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=df,c^2=eg,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 | #35292267, #35317811, #35317812, … |
| maximal normal subgroup of | #35292267, #35317811, #35317812, … |
| maximal quotient of | #35298184, #35304160, #35304170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4126);