Finite Group DatabasebetaFinite Group Databasebeta| order | 1 |
| nilpotency class | 0 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C1 (order 1) · Inn(G) = C1 · Out(G) = C1 |
| holomorph | G ⋊ Aut(G) = C1 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| alternating | A2 |
| symmetric | S1 |
| cyclic | C1 |
| multiplicative | (ℤ/1)ˣ, (ℤ/2)ˣ |
| automorphism group of | C1, C2 |
| holomorph of | C1 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1, 1);