Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12503 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C41 · Schur multiplier (H2) = C2×C8 |
| direct product | C41×#12509 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | #493 |
| commutator, Frattini, cosocle | C4×C8 | C23×C41 |
| prime radical | C41×#1712 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C42×C41 ◁ C82×C41 ◁ G | |
306 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2870 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 5497);