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C₂×#35306 #7628587

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

Aliases

Subgroups

11818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535783);