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C₂×#57180 #8100592

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

Aliases

Subgroups

8418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8007788);