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C₂×#62896 #10586236

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

Aliases

Subgroups

35648 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10493432);