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C₂×#11138 #357832

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

Aliases

Subgroups

2690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265028);