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C₂×#35888 #7629200

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

Aliases

Subgroups

6336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536396);