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C₂×#62899 #10586239

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

Aliases

Subgroups

35284 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)(13,20)(14,17)(15,18)(16,22)(19,24)(21,25)(23,26);(11,13,17,15)(12,18,14,20)(16,21,24,23)(19,25,22,26);(3,4)(5,8)(6,7)(9,10)(11,12,17,14)(13,20,15,18)(16,19,24,22)(21,26,23,25);(5,9)(8,10)(11,14,17,12)(13,20,15,18)(16,22,24,19)(21,26,23,25);(3,5)(4,8)(6,9)(7,10)(11,15,17,13)(12,18,14,20)(16,23,24,21)(19,25,22,26);(3,4)(5,8)(6,7)(9,10)(11,16)(12,19)(13,21)(14,22)(15,23)(17,24)(18,25)(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, 10493435);