Finite Group DatabasebetaFinite Group Databasebeta| order | 11123 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C3×C7×C113 (order 9492) · Inn(G) = C1 · Out(G) = C22×C3×C7×C113 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C11123 |
| abelian | C49×C227 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C7 | C7×C227 |
| socle, prime radical | C7×C227 | C7 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
6 conjugacy classes of subgroups.
11123 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11123, 1);