Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C41 · Schur multiplier (H2) = C25 |
| direct product | D4×SD32×C41 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C41 |
| prime radical | D4×D8×C41 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C4×D4×C41 ◁ C8×D4×C41 ◁ G | |
738 conjugacy classes of subgroups.
2255 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 26835);