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C₂×#8121 #181394

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

Aliases

Subgroups

1624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

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, 88590);