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Cayley diagramAliases
Subgroups
1167 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 22 points:
(1,2);(3,4);(5,6);(7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22);(8,14)(9,21)(10,12)(11,19)(13,17)(16,22)(18,20)
Conjugacy classes & character table
88 conjugacy classes — view the full character table.
Relationships
| Fitting subgroup of | C2×A4×SD32, SD32×AGL(1,𝔽8) |
| maximal subgroup of | #147902, #147909, #147913, … |
| maximal normal subgroup of | #147902, #147909, #147913, … |
| maximal quotient of | C23×#357, C23×#358, C23×#367, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55614);
Finite Group Databasebeta