Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | SD16×Dic166 |
| Sylow | C83 ⋊ Q8×SD16 |
370 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1183 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35393897, #35393906, #35393957, … |
| maximal normal subgroup of | #35393897, #35393906, #35393957, … |
| maximal quotient of | #102×Dic166, #103×Dic166, SD16×Dic83⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17368);