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C₂×#53423 #8102003

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

Aliases

Subgroups

7326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8009199);