Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | #448×D83 |
| Fitting | #448×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#448 |
792 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 155 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 | #1601×D83, #1603×D83, #1604×D83, … |
| maximal normal subgroup of | #1601×D83, #1603×D83, #1604×D83, … |
| maximal quotient of | #1596×D83, #1608×D83, #1599×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13695);