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C₂×#11678 #481337

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

Aliases

Subgroups

952 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 388533);