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C₂×#34954 #7628125

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

Aliases

Subgroups

6566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535321);