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C₂×#11247 #358099

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

Aliases

Subgroups

1766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265295);