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C₂×#35372 #7628727

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

Aliases

Subgroups

7020 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535923);