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C₂×#35207 #7628435

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

Aliases

Subgroups

6314 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)(13,14)(15,16)(17,18)(19,20,23,26)(21,24,22,25);(4,5)(8,9)(12,16)(13,17)(19,20)(21,24)(22,25)(23,26);(3,4,7,5)(6,8,10,9)(11,12,15,16)(13,14,17,18)(19,21,23,22)(20,24,26,25);(3,5,7,4)(6,9,10,8)(11,13,15,17)(12,14,16,18);(3,6,7,10)(4,8,5,9)(11,14)(12,17)(13,16)(15,18)(19,22,23,21)(20,25,26,24)

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, 7535631);