Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #509×D83 |
| Fitting | #509×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#509 |
400 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
688 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/16)×D83, #35557875, #2190×D83, … |
| maximal normal subgroup of | AGL(1,ℤ/16)×D83, #35557875, #2190×D83, … |
| maximal quotient of | #2140×D83, #2139×D83, #2159×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17630);