Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C41 · Schur multiplier (H2) = C22×C4 |
| direct product | C41×#12615 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C41 | C2×D4 |
| commutator | C4 | C2×C4×C8×C41 |
| Frattini, cosocle | C22×C8 | C23×C41 |
| socle | C22×C41 | C8×D4 |
| prime radical | C2×#41×C41 | C2×C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C41 ◁ C22×C16×C41 ◁ G | |
418 conjugacy classes of subgroups.
3608 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 5603);