Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | SD16×C83⋊C8 |
| Sylow | C83 ⋊ C8×SD16 |
180 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×SD16×D83, C2×SD16×C83⋊C8, C8×#14581813, … |
| maximal normal subgroup of | C8×SD16×D83, C2×SD16×C83⋊C8, C8×#14581813, … |
| maximal quotient of | #102×C83⋊C8, #103×C83⋊C8, #106×C83⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3311);