Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×#261 |
| unambiguous semidirect product | D13⋊(C4×D4) |
| Fitting | C2×D4×C13 ⋊ C4 |
| Sylow | C13 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 104 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | #99×#261, #100×#261, #102×#261, … |
| maximal normal subgroup of | #99×#261, #100×#261, #102×#261, … |
| maximal quotient of | C2×C22⋊C4×#261, C2×C4⋊C4×#261, C4×D4×#261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1588);