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C₂×#55105 #8100381

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

Aliases

Subgroups

7792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8007577);