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C₂×#13416 #499081

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

Aliases

Subgroups

1210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406277);