Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | #349×D83 |
| Fitting | #349×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#349 |
236 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 77 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 | #1320×D83, #35313524, #1321×D83, … |
| maximal normal subgroup of | #1320×D83, #35313524, #1321×D83, … |
| maximal quotient of | #1314×D83, #35313464, #1322×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6126);