Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C41 · Schur multiplier (H2) = C26 |
| direct product | C41×#33382 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | C22×D8 |
| commutator | C8 | C23×C4×C41 |
| Frattini, cosocle | C2×C8 | C24×C41 |
| prime radical | C2×C41×#578 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C2×#41×C41 ◁ C2×#131×C41 ◁ G | |
1124 conjugacy classes of subgroups.
2624 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 26370);