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C₂×#49595 #7705162

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

Aliases

Subgroups

7134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7612358);