Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C41 · Schur multiplier (H2) = C23×C4 |
| direct product | C41×#8231 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C2×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C41 |
| Frattini, cosocle | C2×C42 | C23×C41 |
| prime radical | C2×#127×C41 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C43×C41 ◁ G | |
684 conjugacy classes of subgroups.
2132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 1219);