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Cayley diagramAliases
Subgroups
420 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 18 points:
(1,2);(3,4,5,6)(11,12)(13,16)(14,15)(17,18);(7,8,9,10)(12,15)(16,18);(11,13,14,17)(12,16,15,18)
Conjugacy classes & character table
80 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #72268619, #72279676, #72279678, … |
| Frattini subgroup of | #93301, #93373, #93376, … |
| Fitting subgroup of | C2×#376⋊C3, #11710978, #11710980, … |
| maximal subgroup of | C2×#1274, #7855, #7906, … |
| maximal normal subgroup of | C2×#1274, #7855, #7906, … |
| maximal quotient of | C2×C4×#95, C4×#376, C2×#1434, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 999);
Finite Group Databasebeta