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C₂×#35149 #7628371

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

Aliases

Subgroups

24174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535567);