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C₂×#62088 #10578884

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

Aliases

Subgroups

6920 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10486080);