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C₂×#49108 #7704318

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

Aliases

Subgroups

5770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7611514);