Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C41 · Schur multiplier (H2) = C24×C4 |
| direct product | C41×#17380 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C41 | C2×C22⋊C4 |
| commutator | C23 | C23×C4×C41 |
| Frattini, cosocle | C22×C4 | C24×C41 |
| socle | C22×C41 | C22×C22⋊C4 |
| prime radical | C2×#121×C41 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C41 ◁ C22×C42×C41 ◁ G | |
1020 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, 10368);