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C₂×#39728 #7637304

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

Aliases

Subgroups

7284 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7544500);