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C₂×#19721 #6357357

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

Aliases

Subgroups

2346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6264553);