Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4×C41 · Schur multiplier (H2) = C214 |
| direct product | C2×C41×#3428 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C41 | C24 |
| commutator | C2 | C25×C4×C41 |
| Frattini, cosocle | C22 | C26×C41 |
| socle | C23×C41 | C25 |
| prime radical | C23×#41×C41 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C41 ◁ G | |
11534 conjugacy classes of subgroups.
5576 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 55636);