Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C41 · Schur multiplier (H2) = C2 |
| direct product | C41×#7514 |
| subgroup | G/H | |
|---|---|---|
| center | C32×C41 | D4 |
| commutator | C4 | C2×C32×C41 |
| Frattini, cosocle | C2×C32 | C22×C41 |
| socle | C2×C41 | C22⋊C32 |
| prime radical | #41×C41 | C16 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C32×C41 ◁ C2×C32×C41 ◁ G | |
88 conjugacy classes of subgroups.
4592 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 502);