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Cayley diagramAliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 14 points:
(2,3)(4,5)(6,7)(9,10)(11,12)(13,14);(8,9,11,13,14,12,10);(1,2,4,6,7,5,3)
Polycyclic presentation:
2,7^2|b^a=b^6,c^a=c^6
Conjugacy classes & character table
26 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #5997⋊C2, #87658, D72⋊C4, … |
| maximal subgroup of | #5997, D72, C2×C7⋊D7, … |
| maximal normal subgroup of | #5997, D72, C2×C7⋊D7, … |
| maximal quotient of | C7⋊Dic7, C2×C7⋊D7, C3×C7⋊D7, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(98, 4);
Finite Group Databasebeta