Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | D4×C83⋊C16 |
| Sylow | C83 ⋊ D4×C16 |
174 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35316106, D8×C83⋊C16, #35316111, … |
| maximal normal subgroup of | #35316106, D8×C83⋊C16, #35316111, … |
| maximal quotient of | D8×C83⋊C16, SD16×C83⋊C16, Q16×C83⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6330);