Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C83⋊#2104 |
| Sylow | C83 ⋊ #2104 |
178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 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=def,b^2=de,c^2=d,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,f^b=fg,e^c=eg,h^c=h^82925 conjugacy classes — view the full character table.
| maximal subgroup of | #2104×D83, C2×C83⋊#2104, #35435393, … |
| maximal normal subgroup of | #2104×D83, C2×C83⋊#2104, #35435393, … |
| maximal quotient of | #35309545, #35309546, #35309547, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6094);