Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | #456×D83 |
| Fitting | #456×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#456 |
708 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 708 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 | #1405×D83, #35324673, #2203×D83, … |
| maximal normal subgroup of | #1405×D83, #35324673, #2203×D83, … |
| maximal quotient of | #1603×D83, #1609×D83, #1604×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13849);