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C₂×#11329 #358466

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

Aliases

Subgroups

2182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265662);