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C₂×#23424 #6431759

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

Aliases

Subgroups

7794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6338955);