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C₂×#6437463 #72238176

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

Aliases

Subgroups

60597 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

Conjugacy classes & character table

160 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), (13,27)(16,29)(20,31)(23,33), (3,4,8,12)(5,9,15,22)(6,10,17,24)(7,11,19,26)(13,20,27,31)(14,21,28,32)(16,23,29,33)(18,25,30,34), (3,5)(4,9)(6,16,17,29)(7,14)(8,15)(10,23,24,33)(11,21)(12,22)(13,18,27,30)(19,28)(20,25,31,34)(26,32), (3,6)(4,10)(5,13,15,27)(7,18)(8,17)(9,20,22,31)(11,25)(12,24)(14,16,28,29)(19,30)(21,23,32,33)(26,34), (6,17)(7,19)(10,24)(11,26)(14,28)(16,29)(21,32)(23,33));