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C₂×#39042 #7636421

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

Aliases

Subgroups

7230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

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, 7543617);