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C₂×#8115 #181377

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

Aliases

Subgroups

2982 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 88573);