Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | SD64×D83 |
| Fitting | SD64×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×SD64 |
112 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
817 conjugacy classes — view the full character table.
| maximal subgroup of | C2×SD64×D83, #2262×D83, #2263×D83, … |
| maximal normal subgroup of | C2×SD64×D83, #2262×D83, #2263×D83, … |
| maximal quotient of | #1415×D83, #1416×D83, #1424×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6809);