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C₂×#54843 #8102027

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

Aliases

Subgroups

8112 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)(11,12,14,15)(13,17,18,16);(5,9)(8,10)(12,15)(13,18)(19,20,23,24)(21,22,25,26);(4,7)(8,10)(12,15)(16,17)(20,24)(21,25);(3,4)(5,8)(6,7)(9,10)(11,12)(13,16)(14,15)(17,18)(19,21)(20,22)(23,25)(24,26);(3,5)(4,8)(6,9)(7,10)(11,13)(12,16)(14,18)(15,17)(19,22)(20,21)(23,26)(24,25)

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, 8009223);