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C₂×#22607 #6379820

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

Aliases

Subgroups

1990 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6287016);