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C₂×#43675 #7667805

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

Aliases

Subgroups

6160 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)(11,12)(13,17)(14,15)(16,18)(19,20,23,25)(21,24,26,22);(3,4,7,5)(6,9,10,8)(11,13,15,18)(12,16,14,17)(19,21,23,26)(20,22,25,24);(4,5)(8,9)(13,18)(16,17);(3,5,7,4)(6,9,10,8)(11,13)(12,17)(14,16)(15,18)(19,21)(20,24)(22,25)(23,26);(3,6)(4,8)(5,9)(7,10)(11,14,15,12)(13,16,18,17)(19,22,23,24)(20,21,25,26)

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, 7575001);