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C₂×#17541 #6343296

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

Aliases

Subgroups

3778 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 6250492);