Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | #492×D83 |
| Fitting | #492×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#492 |
656 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
946 conjugacy classes — view the full character table.
| maximal subgroup of | #1359×D83, #1409×D83, #1410×D83, … |
| maximal normal subgroup of | #1359×D83, #1409×D83, #1410×D83, … |
| maximal quotient of | #1705×D83, #1706×D83, #1707×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14914);