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C₂×#563 #3528

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

Aliases

Subgroups

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

38 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 2260);