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C₂×#39909 #7637946

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

Aliases

Subgroups

7144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7545142);