Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #2027 |
282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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=d,b^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,c^b=cf,e^b=eg,h^b=h^82,e^c=eg928 conjugacy classes — view the full character table.
| maximal subgroup of | #2027×D83, C2×#24908617, #35431772, … |
| maximal normal subgroup of | #2027×D83, C2×#24908617, #35431772, … |
| maximal quotient of | #35307372, #35307387, #35307392, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5664);