Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1426 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×#7464 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C41 | #367 |
| commutator | C16 | C2×C8×C41 |
| Frattini, cosocle | C4×C16 | C22×C41 |
| socle | C2×C41 | #1372 |
| prime radical | C22×C41 | #368 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C41 ◁ C2×C8×C41 ◁ C4×C8×C41 ◁ C4×C16×C41 ◁ G | |
76 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, 452);