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C₂×#35633 #7629038

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

Aliases

Subgroups

11754 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536234);