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C₂×#24397 #6437742

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

Aliases

Subgroups

5156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344938);