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C₂×#23432 #6431753

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

Aliases

Subgroups

7434 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)(13,22)(14,25)(15,19)(16,20)(17,21)(18,23)(24,26);(4,6)(7,8)(9,10)(11,13,17,14)(12,18,21,26)(15,24,16,23)(19,22,20,25);(8,10)(11,14,17,13)(12,18,21,26)(15,23,16,24)(19,22,20,25);(11,15,17,16)(12,19,21,20)(13,23,14,24)(18,25,26,22)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6338949);