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C₂×#10792 #353380

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

Aliases

Subgroups

4126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260576);