Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | H(3,ℤ/4)×D83 |
| Fitting | H(3,ℤ/4)×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×H(3,ℤ/4) |
404 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 404 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.
946 conjugacy classes — view the full character table.
| maximal subgroup of | #1339×D83, #1340×D83, #35314551, … |
| maximal normal subgroup of | #1339×D83, #1340×D83, #35314551, … |
| maximal quotient of | #1274×D83, #35293801, #35293804, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4209);