Finite Group DatabasebetaFinite Group Databasebeta| order | 5650 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C4×C5×C7×C16 (order 2240) · Inn(G) = C1 · Out(G) = C4×C5×C7×C16 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C5650 |
| abelian | C2×C25×C113 |
| multiplicative | (ℤ/5651)ˣ, (ℤ/11302)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C5 | C2×C5×C113 |
| socle | C2×C5×C113 | C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
12 conjugacy classes of subgroups.
5650 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5650, 1);