Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #1686 |
168 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|b^2=d,c^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,c^b=cf,h^b=h^82,e^c=eg,h^c=h^82802 conjugacy classes — view the full character table.
| maximal subgroup of | #1686×D83, C2×#24906934, #35387015, … |
| maximal normal subgroup of | #1686×D83, C2×#24906934, #35387015, … |
| maximal quotient of | #35297492, #35300635, #35300645, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3981);