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C₂×#60721 #10575346

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

Aliases

Subgroups

6906 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)(13,20)(14,18)(15,25)(16,19)(17,23)(21,22)(24,26);(4,7)(8,10)(11,12)(13,21)(14,25)(15,18)(16,19)(17,24)(20,22)(23,26);(11,13,15,23,16,24,14,22)(12,17,18,20,19,21,25,26);(3,5,6,9)(4,8,7,10)(11,12)(13,17)(14,25)(15,18)(16,19)(20,23)(21,24)(22,26);(11,14,16,15)(12,18,19,25)(13,22,24,23)(17,20,21,26)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482542);