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C₂×#11025 #357519

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

Aliases

Subgroups

4590 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

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, 264715);