Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | #442×D83 |
| Fitting | #442×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#442 |
608 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
946 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/16)×D83, C2×#442×D83, #2943×D83, … |
| maximal normal subgroup of | AGL(1,ℤ/16)×D83, C2×#442×D83, #2943×D83, … |
| maximal quotient of | #1580×D83, #1586×D83, #1594×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13299);