Finite Group DatabasebetaFinite Group Databasebeta| order | 10710 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C32×C4×C16 (order 2304) · Inn(G) = C1 · Out(G) = C22×C32×C4×C16 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C10710 |
| abelian | C2×C5×C7×C9×C17 |
| multiplicative | (ℤ/10711)ˣ, (ℤ/21422)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C2×C3×C5×C7×C17 |
| socle, prime radical | C2×C3×C5×C7×C17 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
48 conjugacy classes of subgroups.
10710 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10710, 1);