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C₂×#62819 #10586166

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

Aliases

Subgroups

35162 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)(14,16)(15,22)(17,21)(18,23)(20,24)(25,26);(5,9)(8,10)(11,13,16,21)(12,17,14,19)(15,20,23,26)(18,24,22,25);(3,4)(5,8)(6,7)(9,10)(11,14,16,12)(13,17,21,19)(15,22,23,18)(20,24,26,25);(11,15)(12,18)(13,20)(14,22)(16,23)(17,24)(19,25)(21,26);(3,5)(4,8)(6,9)(7,10)(11,13)(12,19)(14,17)(15,20)(16,21)(18,25)(22,24)(23,26);(3,4)(5,8)(6,7)(9,10)(11,15)(12,18)(13,20)(14,22)(16,23)(17,24)(19,25)(21,26)

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, 10493362);