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C₂×#60588 #10575122

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

Aliases

Subgroups

7932 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

122 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482318);