Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C41 · Schur multiplier (H2) = C24 |
| direct product | C41×#33509 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C41 | C24 |
| commutator | C22 | C23×C8×C41 |
| Frattini, cosocle | C2×C8 | C24×C41 |
| socle | C22×C41 | C23×C8 |
| prime radical | #121×C41 | C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C41 ◁ G | |
484 conjugacy classes of subgroups.
3116 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 26497);