Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C337 · Schur multiplier (H2) = C22 |
| direct product | #137×C337 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C337 | C2×D4 |
| commutator, Frattini, cosocle | C4 | C23×C337 |
| prime radical | #41×C337 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C337 ◁ C2×C4×C337 ◁ G | |
60 conjugacy classes of subgroups.
3707 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 44);