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Cayley diagramAliases
Splittings
Subgroups
46 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 18 points:
(2,4)(3,7)(5,6)(8,9)(11,13)(12,16)(14,15)(17,18);(10,18,13,16,15,14,12,11,17);(1,9,4,7,6,5,3,2,8)
Polycyclic presentation:
2,3^4|b^3=d^2,c^3=e^2,b^a=b^2d,c^a=c^2e,d^a=d^2,e^a=e^2
Conjugacy classes & character table
42 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #66343⋊C2, #10619734, D92⋊C4, … |
| maximal subgroup of | #66343, D92, C2×C9⋊D9, … |
| maximal normal subgroup of | #66343, D92, C2×C9⋊D9, … |
| maximal quotient of | C9⋊Dic9, C2×C9⋊D9, #92197, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(162, 16);
Finite Group Databasebeta