Finite Group DatabasebetaFinite Group Databasebeta| order | 62506 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 31252 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C62506 |
| abelian | C2×C31253 |
| multiplicative | (ℤ/62507)ˣ, (ℤ/125014)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
4 conjugacy classes of subgroups.
62506 conjugacy classes. The character table is too large to display.
| automorphism group of | C62507 |
| outer automorphism group of | C62507 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(62506, 2);