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C₂×#43224 #7667192

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

Aliases

Subgroups

7322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7574388);