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C₂×#10809 #353510

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

Aliases

Subgroups

2018 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 260706);