Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | #454×D83 |
| Fitting | #454×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#454 |
728 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
688 conjugacy classes — view the full character table.
| maximal subgroup of | #1404×D83, #35324657, #2202×D83, … |
| maximal normal subgroup of | #1404×D83, #35324657, #2202×D83, … |
| maximal quotient of | #1597×D83, #1615×D83, #1598×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13843);