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C₂×#62923 #10586265

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

Aliases

Subgroups

35230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493461);