Finite Group DatabasebetaFinite Group Databasebeta| order | 10051 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C9×C11×C23 (order 9108) · Inn(G) = C1 · Out(G) = C22×C9×C11×C23 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C10051 |
| abelian | C19×C529 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23 | C19×C23 |
| socle, prime radical | C19×C23 | C23 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
6 conjugacy classes of subgroups.
10051 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | C19⋊C3×C529 |
| maximal subgroup of | C2×C19×C529, D19×C529, C19×D529, … |
| maximal normal subgroup of | C2×C19×C529, D19×C529, C19×D529, … |
| maximal quotient of | C2×C19×C529, C3×C19×C529 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10051, 1);