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C₂×#10860 #353647

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

Aliases

Subgroups

2290 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)(13,21)(14,17)(15,19)(16,20)(18,24)(22,25)(23,26);(4,6)(12,17,20,19)(13,22)(18,25,26,21)(23,24);(11,13,15,24,16,22,14,23)(12,18,17,21,20,26,19,25)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260843);