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C₂×#23081 #6382118

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

Aliases

Subgroups

1866 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6289314);