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C₂×#35054 #7628243

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

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, 7535439);