Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C41 · Schur multiplier (H2) = C210 |
| direct product | C22×C41×#408 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C41 | C23 |
| commutator | C22 | C24×C4×C41 |
| Frattini, cosocle | C2×C4 | C25×C41 |
| socle | C24×C41 | C22×C4 |
| prime radical | C23×#41×C41 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C41 ◁ G | |
5326 conjugacy classes of subgroups.
4592 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 53049);