Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C41 · Schur multiplier (H2) = C23×C4 |
| direct product | C41×C4⋊#338 |
| unambiguous semidirect product | C4⋊(C41×#338) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C41 | C2×C42 |
| commutator | C2×C4 | C2×C42×C41 |
| Frattini, cosocle | C23×C4 | C23×C41 |
| socle | C22×C41 | C2×#95 |
| prime radical | C24×C41 | C2×Q8 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C41 ◁ G | |
762 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, 3826);