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C₂×#152716 #72251398

• p-group
• nilpotent
• supersolvable
• solvable
• monomial

Aliases

Subgroups

4621 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,7,12,8,11,20,26)(5,13,15,9,17,22,16,23)(6,10,19,24,18,25,32,34)(14,28,30,33,31,27,29,21);(3,5)(4,9,12,22)(6,14)(7,16,20,15)(8,17)(10,21,24,28)(11,23,26,13)(18,31)(19,29,32,30)(25,33,34,27);(3,6)(4,10)(5,14)(7,19)(8,18)(9,21)(11,25)(12,24)(13,27)(15,30)(16,29)(17,31)(20,32)(22,28)(23,33)(26,34)

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2), (3,4,7,12,8,11,20,26)(5,13,15,9,17,22,16,23)(6,10,19,24,18,25,32,34)(14,28,30,33,31,27,29,21), (3,5)(4,9,12,22)(6,14)(7,16,20,15)(8,17)(10,21,24,28)(11,23,26,13)(18,31)(19,29,32,30)(25,33,34,27), (3,6)(4,10)(5,14)(7,19)(8,18)(9,21)(11,25)(12,24)(13,27)(15,30)(16,29)(17,31)(20,32)(22,28)(23,33)(26,34));