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Cayley diagramAliases
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 1 generator on 19 points:
(1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19)
Conjugacy classes & character table
88 conjugacy classes — view the full character table.
Relationships
| center of | C11×M32, C11×#131, C11×C3⋊C16, … |
| derived subgroup of | D176, #66864, Dic88, … |
| Frattini subgroup of | C121⋊C16, C16×C121, D13552, … |
| Fitting subgroup of | C11⋊C16, C8×D11, #4313, … |
| maximal subgroup of | C11⋊C16, C11×C16, C8×D11, … |
| maximal normal subgroup of | C11⋊C16, C11×C16, C8×D11, … |
| maximal quotient of | C11×C16, C2×C8×C11, C11×C3⋊C8, … |
| automorphism group of | C89, C2×C89 |
| outer automorphism group of | C89, C2×C89 |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(88, 2);
Finite Group Databasebeta