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C₂×#22839 #6380745

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

Aliases

Subgroups

2538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6287941);