Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C83 ⋊ #1747 |
200 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=e,b^2=f,c^2=d,d^2=g,b^a=bd,f^a=fg,e^b=eg,h^c=h^82946 conjugacy classes — view the full character table.
| maximal subgroup of | #35314937, #35314939, #35314944, … |
| maximal normal subgroup of | #35314937, #35314939, #35314944, … |
| maximal quotient of | #35294842, #35294844, #35294846, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4264);