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C₂×#62820 #10586167

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

Aliases

Subgroups

35690 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)(13,19)(14,20)(15,18)(16,17)(21,25)(22,26)(23,24);(5,9)(8,10)(12,17)(13,20)(15,23)(22,25);(3,4)(5,8)(6,7)(9,10)(11,13)(12,14)(15,21)(16,20)(17,19)(18,22)(23,26)(24,25);(11,14)(12,13)(15,22)(16,19)(17,20)(18,21)(23,25)(24,26);(3,5)(4,8)(6,9)(7,10)(11,15,16,23)(12,18,17,24)(13,21,20,26)(14,22,19,25);(3,4)(5,8)(6,7)(9,10)(11,14)(12,13)(15,22)(16,19)(17,20)(18,21)(23,25)(24,26)

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493363);