Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C41 · Schur multiplier (H2) = C24 |
| direct product | C41×#20323 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C41 |
| prime radical | #127×C41 | C23 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C42×C41 ◁ G | |
572 conjugacy classes of subgroups.
1517 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 13311);