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Cayley diagramAliases
Subgroups
868 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 14 points:
(1,2);(4,6)(8,9)(12,13);(7,8,11,9)(10,13,14,12);(3,4)(5,6)(7,9,11,8)(10,13,14,12);(7,10,11,14)(8,12,9,13)
Conjugacy classes & character table
50 conjugacy classes — view the full character table.
Relationships
| Fitting subgroup of | C2×C4⋊(#41⋊C3), #11711027, #11711033, … |
| maximal subgroup of | #8361, #8384, #8385, … |
| maximal normal subgroup of | #8361, #8384, #8385, … |
| maximal quotient of | C2×#2341, C2×Q8×C4⋊C4, C2×#2354, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 2199);
Finite Group Databasebeta