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C₂×#62836 #10586185

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

Aliases

Subgroups

35090 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)(13,22)(14,15)(16,24)(17,18)(19,23)(20,26)(21,25);(5,9)(8,10)(12,18)(13,23)(15,20)(21,24);(3,4)(5,8)(6,7)(9,10)(11,13)(12,19)(14,24)(15,25)(16,20)(17,23)(18,22)(21,26);(11,14)(12,20)(13,24)(15,18)(16,19)(17,26)(21,23)(22,25);(3,5,6,9)(4,8,7,10)(11,15,17,20)(12,14,18,26)(13,25,23,16)(19,24,22,21);(3,4)(5,8)(6,7)(9,10)(11,16,17,25)(12,21,18,24)(13,20,23,15)(14,19,26,22)

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, 10493381);