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C₂×#44129 #7668295

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

Aliases

Subgroups

6728 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7575491);