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Cayley diagramAliases
Subgroups
376 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 16 points:
(1,2,3,4);(5,6)(7,8)(9,10,11,12);(6,8)(13,14,15,16)
Conjugacy classes & character table
80 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #72227437, #72227438, #72267790 |
| Frattini subgroup of | #92825, #92826, #92889, … |
| Fitting subgroup of | C4×#95⋊C3, #11710943, C4×#4622, … |
| maximal subgroup of | #7017, #7028, C4×#327, … |
| maximal normal subgroup of | #7017, #7028, C4×#327, … |
| maximal quotient of | #7554, C4×#336, #10693, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 164);
Finite Group Databasebeta