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C₂×#54197 #8103829

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

Aliases

Subgroups

7396 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)(13,18)(14,17)(15,16)(19,20)(21,24)(22,23)(25,26);(4,5)(8,9)(11,13)(12,17)(14,16)(15,18)(19,21,23,26)(20,24,22,25);(13,14)(17,18)(20,22)(24,25);(3,5,7,4)(6,9,10,8)(11,14,16,13)(12,17,15,18)(19,22,23,20)(21,25,26,24);(3,6,7,10)(4,8,5,9)(11,15,16,12)(13,17,14,18)(19,21)(20,24)(22,25)(23,26)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8011025);