Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | AGL(1,ℤ/8)×D83 |
| Fitting | AGL(1,ℤ/8)×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×AGL(1,ℤ/8) |
298 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
473 conjugacy classes — view the full character table.
| maximal subgroup of | #453×D83, #454×D83, #24916831, … |
| maximal normal subgroup of | #453×D83, #454×D83, #24916831, … |
| maximal quotient of | #418×D83, #417×D83, #428×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 1333);