Finite Group DatabasebetaFinite Group Databasebeta| order | 5642 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C33×C4×C5 (order 2160) · Inn(G) = C1 · Out(G) = C22×C33×C4×C5 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C5642 |
| abelian | C2×C7×C13×C31 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
16 conjugacy classes of subgroups.
5642 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5642, 1);