Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1343 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C41 · Schur multiplier (H2) = C24 |
| direct product | C41×#7250 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | #99 |
| commutator | C22×C4 | C42×C41 |
| Frattini, cosocle | C22×C22⋊C4 | C22×C41 |
| prime radical | C25×C41 | D4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C24×C41 ◁ C22×C22⋊C4×C41 ◁ G | |
632 conjugacy classes of subgroups.
1886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 238);