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C₂×#55014 #8102047

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

Aliases

Subgroups

7186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,7,9)(5,10,6,8)(11,12)(13,17)(14,18)(15,16);(3,5)(4,8)(6,7)(9,10)(11,13,15,18)(12,14,16,17)(19,20,23,24)(21,22,25,26);(5,6)(8,10)(12,16)(14,17)(20,24)(21,25);(3,6,7,5)(4,8,9,10)(11,14)(12,13)(15,17)(16,18)(19,21)(20,22)(23,25)(24,26);(3,4)(5,10)(6,8)(7,9)(11,13)(12,14)(15,18)(16,17)(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, 8009243);