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C₂×#61541 #10576883

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

Aliases

Subgroups

6646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10484079);