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Cayley diagramC112 #1239
Aliases
Subgroups
14 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 22 points:
(1,2,3,4,5,6,7,8,9,10,11);(12,13,14,15,16,17,18,19,20,21,22)
Conjugacy classes & character table
121 conjugacy classes — view the full character table.
Relationships
| center of | D3×C112, D5×C112, C112×A4, … |
| derived subgroup of | C11⋊D11, C112⋊C3, C11⋊Dic11, … |
| Frattini subgroup of | C1212, C112⋊C121, C121⋊C121, … |
| Fitting subgroup of | C11×D11, C11⋊D11, C112⋊C3, … |
| socle of | C11×D11, C11⋊D11, C112⋊C3, … |
| maximal subgroup of | C11×D11, C11⋊D11, C2×C112, … |
| maximal normal subgroup of | C11×D11, C11⋊D11, C2×C112, … |
| maximal quotient of | C2×C112, C3×C112, C5×C112, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(121, 2);
Finite Group Databasebeta