Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C41 · Schur multiplier (H2) = C24 |
| direct product | C41×#13042 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | B(4,𝔽2) |
| commutator | C2×D4 | C22×C4×C41 |
| Frattini, cosocle | C22×D4 | C23×C41 |
| prime radical | C2×H(5,𝔽2)×C41 | C22 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C23×C41 ◁ C22×D4×C41 ◁ G | |
744 conjugacy classes of subgroups.
1640 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 6030);