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Cayley diagramAliases
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 56 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49);(50,51,52,53,54,55,56)
Conjugacy classes & character table
343 conjugacy classes. The character table is too large to display.
Relationships
| center of | #30681061, C72⋊C343, C49⋊C343, … |
| derived subgroup of | C7⋊D49, #11759978, #11759979, … |
| Frattini subgroup of | C49×C343, #30681061, C72⋊C343, … |
| Fitting subgroup of | C7×D49, D7×C49, C7⋊D49, … |
| maximal subgroup of | C7×D49, D7×C49, C7⋊D49, … |
| maximal normal subgroup of | C7×D49, D7×C49, C7⋊D49, … |
| maximal quotient of | C2×C7×C49, C3×C7×C49, C5×C7×C49, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(343, 2);
Finite Group Databasebeta