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C₂×#10706 #353142

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

Aliases

Subgroups

2746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

(1,2);(3,4)(5,6)(7,8,9,10)(11,12)(13,18)(14,17)(15,19)(16,20)(21,24)(22,25)(23,26);(4,6)(12,17,20,19)(18,24,26,25);(11,13,15,22,16,23,14,21)(12,18,19,25,20,26,17,24)

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260338);