Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of #7523 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C41 · Schur multiplier (H2) = C2 |
| direct product | C41×#7526 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C41 | #1404 |
| commutator | #125 | C2×C4×C41 |
| Frattini, cosocle | #491 | C22×C41 |
| prime radical | C22×C41 | AΣL(1,𝔽16) |
| LCS | G ▷ #125 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C22×C41 ◁ C2×C4×C41 ◁ C42×C41 ◁ C41×#491 ◁ G | |
126 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
779 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 514);