Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 7 |
| isoclinism | isoclinic class of D128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C41 · Schur multiplier (H2) = C2 |
| direct product | C41×D128 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C41 | D64 |
| commutator, Frattini, cosocle | C64 | C22×C41 |
| LCS | G ▷ C64 ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C4×C41 ◁ C8×C41 ◁ C16×C41 ◁ C32×C41 ◁ C41×C64 ◁ G | |
46 conjugacy classes of subgroups.
2747 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 539);