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Cayley diagramΓL(1,𝔽64) #67360
Aliases
Splittings
Subgroups
26 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 16 points:
(2,3,4)(5,7,6)(9,13,16,11,12,15)(10,14);(1,2,3,5,4,6,7)(8,16,11,14,12,13,10,9,15)
Polycyclic presentation:
2,3^2,7,3|c^3=e^2,c^a=c^2e,e^a=e^2,c^b=ce,d^b=d^2
Conjugacy classes & character table
22 conjugacy classes — view the full character table.
Relationships
| maximal subgroup of | #67355⋊C2, C2×ΓL(1,𝔽64), C3×ΓL(1,𝔽64), … |
| maximal normal subgroup of | #67355⋊C2, C2×ΓL(1,𝔽64), C3×ΓL(1,𝔽64), … |
| maximal quotient of | #10625392, C2×ΓL(1,𝔽64), #11765603, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(378, 13);
Finite Group Databasebeta