Finite Group DatabasebetaFinite Group Databasebeta| order | 56038 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 28018 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C56038 |
| abelian | C2×C28019 |
| multiplicative | (ℤ/56039)ˣ, (ℤ/112078)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
4 conjugacy classes of subgroups.
56038 conjugacy classes. The character table is too large to display.
| automorphism group of | C56039 |
| outer automorphism group of | C56039 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(56038, 2);