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C₂×#63013 #10586332

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

Aliases

Subgroups

34836 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,8)(6,9)(7,10)(11,12)(13,20)(14,22)(15,18)(16,19)(17,24)(21,23)(25,26);(3,4)(5,8)(6,9)(7,10)(11,13,16,18)(12,15,19,20)(14,21,24,25)(17,23,22,26);(3,5)(4,7)(6,10)(8,9)(11,13,16,18)(12,15,19,20)(14,21,24,25)(17,23,22,26);(11,14)(12,17)(13,21)(15,23)(16,24)(18,25)(19,22)(20,26);(3,5)(4,8)(6,10)(7,9)(11,12)(13,15)(14,17)(16,19)(18,20)(21,23)(22,24)(25,26);(3,4)(5,7)(6,9)(8,10)(11,15)(12,18)(13,19)(14,23)(16,20)(17,25)(21,22)(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, 10493528);