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C₂×#58260 #8104112

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

Aliases

Subgroups

9262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8011308);