Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2180 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C41 · Schur multiplier (H2) = C25 |
| direct product | C2×C41×AGL(1,ℤ/16) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | #442 |
| commutator | C8 | C23×C4×C41 |
| Frattini, cosocle | C2×C8 | C24×C41 |
| prime radical | C2×C41×#509 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C22×C4×C41 ◁ C2×#97×C41 ◁ G | |
710 conjugacy classes of subgroups.
1886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 26455);