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C₂×#14305 #515124

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

Aliases

Subgroups

4350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 422320);