Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | #99×Dic83 |
| Sylow | C83 ⋊ C4×#99 |
412 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 119 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 | #35319535, AΣL(1,𝔽16)×Dic83, #35319540, … |
| maximal normal subgroup of | #35319535, AΣL(1,𝔽16)×Dic83, #35319540, … |
| maximal quotient of | #323×Dic83, #324×Dic83, #35294916, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4300);