← Prev (#67351) Next (#67353) →
Cayley diagramD189 #67352
Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 34 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27)(28,29,30,31,32,33,34);(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(29,34)(30,33)(31,32)
Polycyclic presentation:
2,3,7,3^2|b^3=d^2e,d^3=e^2,b^a=b^2d,c^a=c^6,d^a=d^2e,e^a=e^2
Conjugacy classes & character table
96 conjugacy classes — view the full character table.
Relationships
| maximal subgroup of | D7×D27, C2×D189, D567, … |
| maximal normal subgroup of | D7×D27, C2×D189, ΓL(1,𝔽8)⋊D27, … |
| maximal quotient of | Dic189, C2×D189, D567, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(378, 5);
Finite Group Databasebeta